Question

A triangle is drawn and squares are created from the lengths of each side. Square A has an area of 18 units 2 and Square B has an area of 90 units2 . What must be the area of the 3rd square for triangle to have a right angle?

Answer 1

To find the area of the third square, we need to find the length of the third side of the triangle. Let's assume the side lengths of the triangle are a, b, and c, and the areas of the squares are A, B, and C respectively.

We know that the area of a square is equal to the square of its side length. So we have:

A = a^2
B = b^2
C = c^2

We are given the areas of squares A and B:

A = 18 units^2
B = 90 units^2

We can set up an equation using the Pythagorean theorem:

a^2 + b^2 = c^2

Substituting the areas of the squares, we get:

18 + 90 = c^2

108 = c^2

Taking the square root of both sides, we find:

c = √108

Simplifying, we get:

c = 6√3 units

To find the area of the third square, we square the side length:

C = (6√3)^2

C = 36 * 3

C = 108 units^2

Therefore, the area of the third square must be 108 square units for the triangle to have a right angle.