Question

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, 4 feet, and 3 feet? note that the area of a square is s², where s is the side - length.

Explanation:

Step1: Calculate area of first small square

Let the side - length of the first small square $s_1 = 4$ feet. Using the formula $A = s^{2}$, the area $A_1=s_1^{2}=4^{2}=16$ square feet.

Step2: Calculate area of second small square

Let the side - length of the second small square $s_2 = 3$ feet. Using the formula $A = s^{2}$, the area $A_2=s_2^{2}=3^{2}=9$ square feet.

Step3: Calculate sum of areas of small squares

The sum of the areas of the two small squares $A_{sum}=A_1 + A_2=16 + 9=25$ square feet.

Step4: Calculate area of large square

Let the side - length of the large square $s_3 = 8$ feet. Using the formula $A = s^{2}$, the area $A_3=s_3^{2}=8^{2}=64$ square feet.

Step5: Compare the areas

Since $25
eq64$, the sum of the areas of the two smaller squares is not equal to the area of the large square.

Answer:

No