An area, A, consisting of the sum of two squares is 1000. The side of one square is 10 less than 2/3 of the side of the other square. What are the sides of the squares?

Answer 1

Let x,y be the side of each of the squares.

x² + y² = 1000
y=(2/3)x-10

substitute (2/3)x-10 for y in the first equation:
x² + ((2/3)x-10)² = 1000

Expand and solve for the quadratic equation to get x=30 or x=-270/13.
Reject second solution to get x=30, y=10