Question

1. is the sum of the areas of two smaller squares equal to the area of a large square if the side lengths of the squares are 8 feet, 5 feet, and 3 feet? note that the area of a square is $s^{2}$, where $s$ is the side length. explain.

Explanation:

Step1: Calculate the area of each square

The area of a square is \(s^{2}\).
For the square with side - length \(s = 3\) feet, the area \(A_1=3^{2}=9\) square feet.
For the square with side - length \(s = 5\) feet, the area \(A_2 = 5^{2}=25\) square feet.
For the square with side - length \(s = 8\) feet, the area \(A_3=8^{2}=64\) square feet.

Step2: Calculate the sum of the areas of the two smaller squares

The sum of the areas of the two smaller squares is \(A_1 + A_2\).
\(A_1+A_2=9 + 25=34\) square feet.

Answer:

Since \(34
eq64\), the sum of the areas of the two smaller squares (\(3\) - foot and \(5\) - foot side - length squares) is not equal to the area of the \(8\) - foot side - length square.