Answer:
50.75 units
Step-by-step explanation:
In this problem
Triangles HFM and PST are similar
we know that 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
[tex]z=\frac{HF}{PS}[/tex]
substitute the given values
[tex]z=\frac{14}{8}=1.75[/tex]
step 2
Find the perimeter of triangle PST
[tex]P=8+9+12=29\ units[/tex]
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
[tex]29(1.75)=50.75\ units[/tex]
