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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