Question

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.

Answer 1

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

Answer 2

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

Answer 3

let the longer side be x and the shorter side by y and diagonal = d
then the hypotenuse is √(x^2 + y^2)
d=2/3x+y
(2/3x+y)2 = (x^2 + y^2)
y/x = 5/12