Question

An artist is creating a scale drawing of a mural in the shape of a right triangle she will paint for the city. Her drawing is 8 inches long and has a hypotenuse of 15 inches. If the mural has a hypotenuse of 96 inches, how long is the mural?

Answer 1

We can use ratios to solve this problem. If we let x be the length of the hypotenuse of the mural, then we can set up the following proportion:

8/15 = x/96

To solve for x, we can cross-multiply and simplify:

8 × 96 = 15 × x
768 = 15x
x = 768/15
x ≈ 51.2

Therefore, the length of the mural is approximately 51.2 inches.

Answer 2

51.2 inches

Explanation:

You want the length of a mural whose hypotenuse is 96 inches if the scale drawing has a length of 8 inches and a hypotenuse of 15 inches.

Ratios

The ratios of corresponding lengths will be the same:

drawing length / drawing hypotenuse = mural length / mural hypotenuse

8 in / 15 in = mural length / 96 in

Solution

Multiplying the equation by 96 in, we have ...

(96 in)·8/15 = mural length

51.2 in = mural length

The mural is 51.2 inches long.