Question

A square has a side length of 10 inches. Congruent isosceles right triangles are cut off each corner so that the resulting octagon has equal side lengths. How many inches are in the length of one side of the octagon

Answer 1

The length of the side of the octagon is 4.142 inches.

We can find the length of the sides of the octagon as follows:

Let the length of the congruent sides of the isosceles triangle be x.

The hypotenuse of the triangle is given by:

√x+x = √2x

This is also the length of the sides of the octagon. It is given that the sides of the octagon are equal.

It is also given that the length of the square side is 10 inches.

This means that:

x + √2x + x = 10

2x + √2x = 10

(2 + √2)x = 10

(2 + 1.414)x = 10

3.414x = 10

x = 10/3.414

x = 2.929 inches.

The side of the octagon is given by:

√2 × 2.929 = 4.142 inches

Therefore, we have found that the length of the sides of the octagon is 4.142 inches.

Learn more about octagons here: https://brainly.com/question/358118

#SPJ4