SOLUTION: Working on my math homework and can't figure this one out. The lengths of the legs of a right triangle are x and 3x+y. The length of the hypotenuse is 4x-y. Find the ratio of x

Algebra ->  Pythagorean-theorem -> SOLUTION: Working on my math homework and can't figure this one out. The lengths of the legs of a right triangle are x and 3x+y. The length of the hypotenuse is 4x-y. Find the ratio of x       Log On


   

Question 124099This question is from textbook Geometry for Enjoyment and Challenge
: Working on my math homework and can't figure this one out.
The lengths of the legs of a right triangle are x and 3x+y. The length of the hypotenuse is 4x-y. Find the ratio of x to y. This question is from textbook Geometry for Enjoyment and Challenge

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
The lengths of the legs of a right triangle are x and 3x+y. The length of the hypotenuse is 4x-y. Find the ratio of x to y.
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Use Pythagoras to get:
(4x-y)^2 = x^2 + (3x+y)^2
16x^2-8xy+y^2 = x^2 + 9x^2+6xy+y^2
6x^2 = 14xy
6x = 14y
x/y = 7/3
Ratio is 7:3
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Cheers,
Stan H.