Question

A square is inscribed in an isosceles right triangle. Length of the leg equals to 2 in. as shown on the figure. Find the perimeter of the square.

Please help

Answer 1

The perimeter of the square is
`4\ in`

Explanation:

Let

x----> the length side of the square

we know that

In an isosceles right triangle the measures of the internal angles are 45°-90°-45°

so

the horizontal distance is equal to the vertical distance

`2=x+x`

`x=1\ in`

The perimeter of the square is

`P=4b`

we have

`b=1\ in`

substitute

`P=4(1)=4\ in`