Question

the ratio of one side of abc to the corresponding side of similar def is 5:8. if the perimeter of def is 96 inches, what is the perimeter of abc?

Answer 1

Answer:

Perimeter of abc is 60 inches.

Step-by-step explanation:

The ratio of one side of triangle abc to the corresponding side of similar triangle def is 5:8.

Now we are given that the perimeter of def is 96 inches.

since the perimeter is the sum of all the sides of a triangle.

" If two similar triangles have a scale factor of a : b, then the ratio of their perimeters is a : b" .

Here we have a=5 and b=8.

Hence by the above statement we could say that:

Let Perimeter of abc be denoted by "P"

Perimeter of abc : Perimeter of def=5:8

⇒  $\dfrac{P}{96}=\dfrac{5}{8}\\\\P=\dfrac{5\times96}{8}\\\\P=60$

Hence the Perimeter of abc is 60 inches.