Question

A triangle is drawn and squares are created from the lengths of each side.
Square A has an area of 30 units ^2 and square B has an area of 37 units ^2.
What must be the area of the 3rd square for the triangle to have a right angle?
The area of square C is

Answer 1

To determine the area of the third square (square C) for the triangle to have a right angle, we can use the Pythagorean theorem. In a right triangle, the sum of the areas of the two smaller squares (corresponding to the two shorter sides) is equal to the area of the largest square (corresponding to the hypotenuse).

Let:
- Area of square A = \( 30 \) units²
- Area of square B = \( 37 \) units²
- Area of square C (the square corresponding to the hypotenuse) = \( A_C \)

According to the Pythagorean theorem:

\[
A_C = A + B
\]

To find the area of square C, we can just sum the areas of squares A and B:

\[
A_C = 30 + 37
\]
\[
A_C = 67
\]

Thus, the area of square C must be \( 67 \) units² for the triangle to have a right angle.