Question

Sophia has 52 identical isosceles right triangles. She wants to make a square using some of them. How many different sized squares can she make?

Answer 1

Answer:

A maximum of 3 different sized squares can be formed from the 52 identical isosceles right triangles.

Step-by-step explanation:

A square is a plane shape that has the length of all its sides to be equal. While an isosceles triangle is one that has two equal sides and angles. A right angle isosceles triangle has a right angle, while other two angles are $45^{0}$ each.

To form a square, 2 right angles isosceles triangles are required. Since there are 52 identical isosceles right triangles, the number of different sized squares she would make would be:

The number of triangles required to form different sized squares are;

the first square requires 2 triangles

the second square of different size requires 8 triangles

the third square of different size requires 18 triangles

So that, 2 + 8 + 18 = 28 triangles has been used. But the next square would require 32 triangles.

Therefore, 3 different sized squares can be formed from the 52 identical isosceles right triangles.