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In a certain right triangle, the hypotenuse equals (x+z) while the other two sides are (x+y) and (y+z) for positive integers x, y, z.  If y+4=z and z>x , then compute z/x.

 

 Dec 29, 2020
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We see that z=y+4

 

using Pythagorean theorem, we find that (x+y)^2+(y+z)^2=(x+z)^2, 

plugging in the equation for 2 variables, we get 

(x+y)^2+(2y+4)^2=(x+y+4)^2


if we simplify the above equation of two variables, then you should get

y^2+2y=2x

now use some trial and error on y and see if x and z will satisfy, hint: there is only one solution

 Dec 29, 2020

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