Posted by JEFF BOMB on Tuesday, January 5, 2010 at 8:10pm.
Abigail Adventuresome took a shortcut along the diagonal of a rectangular field and saved a distance equal to 1/3 the length of the longer side.Find the retio of the length of the shorter side of the rectangle to that of the longer side.

Math  Reiny, Tuesday, January 5, 2010 at 9:47pm
let the longer side be x and the shorter side by y
then the hypotenuse is √(x^2 + y^2)
We are told
√(x^2 + y^2) = x + x/3
√(x^2 + y^2) = 4x/3
square both sides
x^2 + y^2 = 16x^2/9
9x^2 + 9y^2 = 16x^2
9y^2 = 7y^2
take √ of both sides, using only the positive case
3y = (√7)x
y/x = √7/3
y:x = √7 : 3

Math  laura, Monday, March 22, 2010 at 9:47pm
that actually is wrong because i found the answer to that in the back of my book and the answer is 5/12, but i have no idea how to get to that answer
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