A right triangle has legs measuring 5 feet and 12 feet. If the legs of the triangle were doubled, what would be the difference in the original and enlarged perimeters?

Answers

Answer 1

Answer:

[tex]30[/tex]

Step-by-step explanation:

1. Approach

First, use the Pythagorean theorem to solve for the hypotenuse of the given right triangle. Then find the perimeter by adding up the values of all the sides. The problem then has the lengths of the legs doubled. When the legs undergo a scaling factor, the hypotenuse and perimeter undergo the same scaling factor. Here, the legs are doubled, hence the hypotenuse and the perimeter are also doubled. Finally, subtract the new perimeter from the original perimeter.

2. Find the original hypotenuse

Remember the Pythagorean theorem states;

[tex]x^{2}+y^{2}=z^{2}[/tex]

Where (a) and (y) are the legs (or the sides adjacent to the right angle), and (z) is the hypotenuse or the side opposite to the right angle.

Substitute in the given value and solve,

[tex](5)^{2}+(12)^{2}=z^{2}\\\\25 + 144 = z^{2}\\\\169=z^{2}\\\\\sqrt{169}=z\\\\13=z[/tex]

3.Find the perimeter of the original triangle

To find the perimeter of a polygon, one must add up the lengths of all the sides.

[tex]5 + 12 + 13\\\\= 30[/tex]

4. Find the new perimeter

In a right triangle, when both legs undergo a scaling factor, the hypotenuse also has the same change, and the perimeter also undergoes the same change. In this case, the length of the legs is doubled, therefore, the hypotenuse and the perimeter are also doubled.

New hypotenuse; [tex]26[/tex]

New perimeter; [tex]60[/tex]

5. Find the difference

Now all that is left is to subtract the new perimeter from the original perimeter;

(New_perimeter) - (original_perimeter)

= [tex]60 - 30[/tex]

= [tex]30[/tex]


Related Questions

A number is being multiplied by a power of 10. Find the number.

Enter your answers in the boxes.

Can you guys help me :D ty

Answers

Answer: a:7 b:36 c:4

Step-by-step explanation:

the exponents are the amount of 0s you put behind the number.

ex: 10 to the power of 4: 10,000, 4 zeroes.

fourteen cups of tomato sauce makes 30 servings of spaghetti. How many cups are needed for 45 servings?

Answers

Answer:

28 cups

Step-by-step explanation:

Factor by grouping plz show steps!

Answers

Answer:

Step-by-step explanation:

4y(y^2+6)+7(y^2+6)

answer:(4y+7)(y^2+6)

Graph the solution of this inequality

Answers

Answer:

third one

Step-by-step explanation:

Factor each expression

49g +63y

wrong answers= reported
if u don't know don't ANSWER

Answers

Answer:

7 ( 7 g + 9 y )

Step-by-step explanation:

thats the answer

Answer:

The answer is 7(7g + 9y).

Step-by-step explanation:

Factor 7 out of 49g + 63y.

~Hoped this helped~

Brainly, please?

i know it is easy but help me

Answers

Answer:

it's 7

Step-by-step explanation:

the one side is equal to the other side do it's 7

Answer:

3

Step-by-step explanation:

7x12 = 84

252/84 = 3

7x12x3=252

On a coordinate plane, how are the locations of the points (7 , -9) and (-7 , 9) related?

Answers

Answer:

11 units.

They both are on the x axis of 9. The distance between -7 and 4 is 11 units, therefore that is why the answer is 11.

Step-by-step explanation:

They are reflected over the x axis.

A vending machine has $50.40 in it. There are 432 coins total and the machine only accepts nickels and quarters. How many nickels and quarters are in the machine?​

Answers

Nickels = n
Quarters = q

n + q = 432

Nickels are 5 cents (0.05)
Quarters are 25 cents (0.25)

0.05n + 0.25q = 50.40

Use substitution or elimination (I like substitution)
n + q = 432 means n = 432 - q

So 0.05n + 0.25q = 50.4 is
0.05(432 - q) + 0.25q = 50.4
21.6 - 0.05q + 0.25q = 50.4
21.6 + 0.2q = 50.4
0.2q = 28.8
q = 144

Plug in to find nickels
n + q = 432 means
n + 144 = 432
n = 288

PLEASE HELP! GIVING POINTS!

Answers

I think it’s C, 17/20
your answer should be C.

Z-Grand Shipping Company manufactures boxes in the shape of a cube.
The formula for the surface area of a cube is 6s, where s is the length of one side.
Z-Grand Shipping Company manufactures large boxes with a side length of 6 feet. The surface area of each large box is
square feet
The company also manufactures small boxes with a side length of 3 feet. The surface area of each small box is
square feet
The surface area of the large box is times larger than the small box.

Answers

Answer:

Z-Grand Shipping Company manufactures boxes in the shape of a cube.

The formula for the surface area of a cube is 6s, where s is the length of one side.

Z-Grand Shipping Company manufactures large boxes with a side length of 6 feet. The surface area of each large box is 216

square feet

The company also manufactures small boxes with a side length of 3 feet. The surface area of each small box is 54

square feet

The surface area of the large box is 4 times larger than the small box.

{So for the first line which is The surface area of each large box is

square feet.}

Ans;216

{The second line which is The surface area of each small box is

square feet.]

Ans;54

{The Third line which is The surface area of the large box is times larger than the small box.}

Ans;4

Thank you So much Hope this helps you! Please Mark Brainleast looking forward to help everyone ty!

The surface area of each small box is 54 square feet and each large box is 216 square feet.

What is the area of cube?

The formula for the surface area of a cube is 6s, where s is the length of one side.

We are given that Z-Grand Shipping Company manufactures large boxes with a side length of 6 feet.

The surface area of each large box is 216 square feet

The company also manufactures small boxes with a side length of 3 feet. The surface area of each small box is 54 square feet

The surface area of the large box is 4 times larger than the small box.

The surface area of each large box = 216 square feet.}

The second line which is The surface area of each small box is

= 54 square feet.

The Third line which is surface area of the large box is times larger than the small box is;

4

Learn more about the area;

https://brainly.com/question/1658516

#SPJ2

how to do two digits multiplication

Answers

Search it up! There are lots of helpful and informative videos that can explain how to do it more than I can!

i hope this helps :)

Q2: Select the correct answer to each of the questions.
Vertex
X-Intercept
Axis of
Symmetry
Parabola
What divides a
parabola into 2
symmetrical
halves?
The graph of a
quadratic
function is called
a...?
What do we call
the
highest/lowest
point of a
quadratic?
O

Answers

I need a pic for this

a boat traveled 19 kilometers east and 53 kilometers south, how far from its starting position is it?

A 25-foot ladder rest against a house at a point 24.1 feet above the ground. How far away from the house is the base of the ladder?​

Answers

Answer:

56.3

6.6

Step-by-step explanation:

Answer:

A boat traveled 19 kilometers east and 53 kilometers south, how far from its starting position is it?: √3170≈56.3 km.

A 25-foot ladder rest against a house at a point 24.1 feet above the ground. How far away from the house is the base of the ladder?: √44.19≈6.65 ft.

Step-by-step explanation:

For these questions, we will need to use the pythagorean theorem: a²+b²=c², where a and b are the legs of the right triangle and c is the hypotenuse.

A boat traveled 19 kilometers east and 53 kilometers south, how far from its starting position is it?

In this question, we are looking for the hypotenuse.

19 and 53 are the legs of the triangle, so we can plug it into the equation:

19²+53²=c²

361+2809=c²

3170=c²

√3170=c

56.30275304103699, or approximately 56.3 km.

A 25-foot ladder rest against a house at a point 24.1 feet above the ground. How far away from the house is the base of the ladder?​

25 is the hypotenuse since it is leaning sideways and is the longest side. 24.1 is one of the legs.

In this question, we are looking for one of the legs.

Let's plug it in: 24.1²+b²=25²

580.81+b²=625

Subtract 580.81 from both sides.

b²=44.19

b=√44.19

6.647555941848102, or approx. 6.65 ft.

The height of a male athlete testing his vertical jump can be modeled by h = − 16t ^2 + 14t. The height is h and the time is t. How many seconds is he in the air?

Answers

Answer:

0.88 (I think this is how Mrs. Futch wants it to be written)

Step-by-step explanation:

h=-16t^2+14t

(Substitute h with 0)

0=-16t^2+14t

(Factor)

0=2t(-8t+7)

2t=0               -8t+7=0

t=0                  t=0.88

{0, 0.88}

(John Komperda)

just answer with the scale factor pleaseee ​

Answers

1.5 :)

Step-by-step explanation:

you would divide the 2 numbers, then youre left with the sf

Help please if you can....

Answers

Answer:

C

Step-by-step explanation:

Jeanie likes mixing leftover salad dressings together to make new dressings. She
combined 0.55 L of a 90% vinegar salad dressing with 0.45 L of another dressing to
make 1 L of salad dressing that is 60% vinegar. What percent of the second salad
dressing was vinegar?

Answers

Answer:

23%

im supposed to add more to this so i can submit this so here you go

The length of rectangle A is one third the length of rectangle B. If the length of rectangle B is 36 inches, what is the length of rectangle A in inches?

Answers

Answer:

The length of rectangle A is 12 in

36 / 3 = 12

Hope this helps.

Answer:

36 itdb36 i think ye sit is

Step-by-step explanation:

These questions both go together if you answer them I'll give you brainliest !! :)

Answers

Answer: the answer is 2.5

Step-by-step explanation:

I just did that

On my bike, I was able to travel 40 miles in one hour. From this information, we can determine the bike's (2 points)
a
speed
Ob
velocity
ос
acceleration
Od
direction

Answers

speed i think! sorry if im wrong!

The Sales in thousands of a new type of product, headphones that block out annoying people, are given by S(t)= 230-60e^-0.1t, where t represents time on months.

A. Find the sales at the time when t=4 months.
B. AFter how many months will sales be equal to $220,000.

Answers

Answer:

A) 15.33

B) 843333.33

Step-by-step explanation:

PLZZ HELP bubba biked 19 kilometers how far did he bike in miles? A mile is approximately 1.6 kilometers Round to the nearest tenth

Answers

11.8 miles............

Answer:

11.9 miles

Step-by-step explanation:

1.6 kilometers = 1 mile

19 kilometers = 1/1.6 * 19 miles

= 11.875 miles

Graph - 2x + 4y = 16 using
intercepts.

Answers

Answer:

y intercept is -1/2

Step-by-step explanation:

Step-by-step explanation:

here you go love use an app it tells you everything

8 is subtracted from a number,and then the difference is multiplied by 2.the result is 24.find the number

Answers

Answer:

20

Step-by-step explanation:

suppose the number is x

so

(x-8) * 2 =24

x-8=12

x=12+8

x=20

the question is in the picture below​

Answers

Answer:

The missing value is [tex]14[/tex].

Step-by-step explanation:

Divide the known denominator by its numerator.

[tex]4\div2=2[/tex]

Now multiply the quotient by the other numerator ([tex]7[/tex]).

[tex]2×7=14[/tex]

or

First, find the factor by which the numerators have been multiplied.

[tex]2x=7→x=3.5[/tex]

Now, do the same for the denominators.

[tex]4(3.5)=14[/tex]

Find the missing length.
8
7
C
✓ [?]
C =
Pythagorean Theorem: a2 + b2 = c2
Enter

Answers

Answer:

√113

Step-by-step explanation:

8*8 + 7*7 = c^2

64 + 49 = c^2

√113 =C

SOMEONE PLEASE HELP. what is the ratio then what is the ratio in a simplified fraction? PICTURE

Answers

Answer:

3/8 to 2

Step-by-step explanation:

If 6r + 7 = 13 + 7r, then what is the value of 4r ?

Answers

Answer:

r=-6

Step-by-step explanation:

Answer:

4r = -24

Step-by-step explanation:

6r + 7 = 13 + 7r

6r = 6 + 7r

-r = 6

r = -6

4r = -24

what is 0.375 we a fraction in simplest form?
1/8
3/8
5/16
2/5

Answers

the answer is 3/8.......

which value of x makes the inequality 3x+3>15

Answers

Answer:

x>4

Step-by-step explanation:

3x+3>15

3x>15-3

3x>12

x>12/3

x>4

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