SOLUTION: An area of 52 square feet is to be enclosed by two squares whose sides are in the ratio of 2:3.Find the sides of the two squares.

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Question 229539: An area of 52 square feet is to be enclosed by two squares whose sides are in the ratio of 2:3.Find the sides of the two squares.
Answer by ankor@dixie-net.com(12700) About Me  (Show Source):
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An area of 52 square feet is to be enclosed by two squares whose sides are in the ratio of 2:3.
Find the sides of the two squares.
:
Let x = side of one square
Let y = side of the other squares
then
x%2Fy = 2%2F3
therefore
2y = 3x
y = 3%2F2x
y = 1.5x
:
Area of the two squares:
x^2 + y^2 = 52
Replace y with 1.5x
x^2 + (1.5x)^2 = 52
x^2 + 2.25x^2 = 52
3.25x^2 = 52
x^2 = 52%2F3.25
x^2 = 16
x = sqrt%2816%29
x = 4 ft side of one square
and
y = 1.5(4)
y = 6 ft side of the other square
;
:
Check solution: 4^2 + 6^2 = 52