Question

a triangle is reduced.
image of two triangles: pink triangle with 12 in (height), 16 in (base), 20 in (hypotenuse); blue triangle with 9 in (height), 12 in (base). text: not drawn to scale
what is the perimeter of the reduced triangle, in inches?
options: 15, 21, 36, 48

Explanation:

Step1: Determine the scale factor

The original triangle has a height of 12 in and the reduced triangle has a height of 9 in. The scale factor $k$ is $\frac{9}{12}=\frac{3}{4}$.

Step2: Find the hypotenuse of the reduced triangle

The original hypotenuse is 20 in. Using the scale factor, the hypotenuse of the reduced triangle is $20\times\frac{3}{4} = 15$ in.

Step3: Calculate the perimeter of the reduced triangle

The sides of the reduced triangle are 9 in, 12 in, and 15 in. The perimeter $P$ is $9 + 12 + 15 = 36$ in.

Answer:

36