Question

scale factors (11/26)
a triangle is reduced.
not drawn to scale
what is the perimeter of the reduced triangle, in inches?
hint: this is a 2 - step problem. you need to find the missing side before you find the perimeter.
15
21
36
48

Explanation:

Step1: Find the scale factor

The original triangle has a side of 12 in, and the reduced triangle has the corresponding side of 9 in. The scale factor \( k \) is \( \frac{9}{12}=\frac{3}{4} \).

Step2: Find the missing side 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