The length of each side of a square is 3 in. more than the length of each side of a smaller square. the sum of the areas of the squares is 65 in^2. find the lengthy the sides of the two squares.

Question

The length of each side of a square is 3 in. more than the length of each side of a smaller square. the sum of the areas of the squares is 65 in^2. find the lengthy the sides of the two squares.

Answer 1

(3+s)^2 + s^2 = 65

9 +6s +s^2 +s^2 = 65

2s^2 + 6s - 56 = 0

s^2 + 3s -28 = 0

(s + 7)(s-4) = 0

s = 4 inches for the side of the smaller square

s+3 = 7 inches = the side of the larger square

7^2 + 4^2 = 49 + 16 = 65 in^2