10

A triangle is drawn and squares are created from the lengths of each side.

Square A has an area of
7

units
2
7 units
2
and Square B has an area of
31

units
2
.
31 units
2
.

What must be the area of the 3rd square for triangle to have a right angle? Click Here for Help Video.

The area of Square C is

units
2
.
units
2
.

1 answer

In a right triangle, the squares of the lengths of the two shorter sides (let's call them Square A and Square B) must add up to the square of the length of the hypotenuse (Square C). This is a consequence of the Pythagorean theorem.

Given:

  • Area of Square A = 7 units²
  • Area of Square B = 31 units²

To find the area of Square C (the hypotenuse), we use the equation:

\[ \text{Area of Square C} = \text{Area of Square A} + \text{Area of Square B} \]

Substituting the given areas:

\[ \text{Area of Square C} = 7 + 31 = 38 \]

Thus, the area of Square C is \( 38 \) units².