Question

What is the ratio of the perimeter of ΔHKO to the perimeter of ΔFGO

?

Express your answer as a simplified fraction.

Enter your answer in the box.

Answer 1

Part 1) The ratio of the perimeter of ΔHKO to the perimeter of ΔFGO is
`(1)/(2)`

Part 2) The ratio of the area of ΔKHO to the area of ΔGFO is
`(1)/(4)`

Explanation:

Part 1)

we know that

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

In this problem

Triangles HKO and FGO are similar by AAA Theorem

Find the scale factor

The scale factor is equal to the ratio of its corresponding sides

`(4)/(8)=(7)/(14)=(1)/(2)`

Part 2) Find the ratio of the area of ΔKHO to the area of ΔGFO

Area of ΔKHO

`A=4*7/2=14\ units^(2)`

Area of ΔGFO

`A=8*14/2=56\ units^(2)`

The ratio of its areas is equal to

`(14)/(56)=(1)/(4)`

Alternative Method

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

In this problem we have that

The scale factor is
`(1)/(2)`

so

squared the scale factor

`((1)/(2))^(2)=(1)/(4)` ----> is correct