Question

Angle $eab$ is a right angle, and $be = 9$ units. what is the number of square units in the sum of the areas of the two squares $abcd$ and $aefg$?

Answer 1

Let the measure of side AB be x, then, the measue of side AE is given by

$AE=\sqrt{9^2-x^2}$.

Now, ABCD is a square of size x, thus the area of square ABCD is given by

$Area=x^2$

Also, AEFG is a square of size $\sqrt{9^2-x^2}$, thus, the area of square AEFG is given by

$Area=\left(\sqrt{9^2-x^2}\right)^2=9^2-x^2=81-x^2$

The sum of the areas of the two squares ABCD and AEFG is given by

$x^2+81-x^2=81$

Therefore, the number of square units in the sum of the areas of the two squares ABCD and AEFG is 81 square units.