The area of a rectangle is 45 cm2. Two squares are constructed such that two adjacent sides of the rectangle are each also the side of one of the squares. The combined area of the two squares is 106 cm². Find the lengths of the sides of the squares.

Answer 1

If the two squares are x and y, then
xy = 45
x^2 + y^2 = 106
so,
x^2 + (45/x)^2 = 106
x^2 + 2025/x^2 = 106
x^4 - 106x^2 + 2025 = 0
(x^2-25)(x^2-81) = 0
x^2 = 25 or 81
x = 5 or 9
yep, 5*9 = 45