ANSWER

The answer and solution to the question posed in an earlier post is provided here.


Ans. 10 and 30 (10² + 30² = 1000)

The sides of the squares are x and y.
x2 + y2 =1000
y = 2/3x -10: Squaring yields
y2 =4/9x2 - 2(2/3x X 10) + 100
y2 = 4/9x2 - 40/3x + 100
Substitution into the first equation yields
13/9x2 – 40/3x – 900 = 0
13x2 -120x - 900 = 0
(x+270) (x+30) = 0
Either x+270=0 or x+30=0
302 + y2 = 1000
900 + y2 = 1000
y2 = 100
y = 10
x = 30