Question

△HFM ~ △PST

Answer 1

Answer:

The perimeter of △HFM is 50.75 units

Step-by-step explanation:

The picture of the question in the attached figure

In this problem

Triangles HFM and PST are similar

we know that

If two figures are similar, then the ratio of its corresponding sides is proportional, and this ratio is called the scale factor

step 1

Find the scale factor

Let

z ----> the scale factor

$z=\frac{HF}{PS}$

substitute the given values

$z=\frac{14}{8}=1.75$

step 2

Find the perimeter of triangle PST

$P=8+9+12=29\ units$

step 3

Find the perimeter of triangle HFM

we know that

If two figures are similar, then the ratio of its perimeters is equal to the scale factor

so

The perimeter of triangle HFM is equal to the perimeter of triangle PST multiplied by the scale factor

so

$29(1.75)=50.75\ units$