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The side lengths of a right triangle measure x, x + y, and x + 2y units where 0 < y < x. What is the value of y/x? Express your answer as a common fraction

 Jul 4, 2022
 #1
avatar+1155 
+10

catmg's answer:

(x)^2 + (x+y)^2 = (x + 2y)^2 (this is the pythagreon theorum)

x^2 + x^2 + y^2 + 2xy = x^2 + 4y^2 + 4xy

2x^2 + y^2 + 2xy = x^2 + 4y^2 + 4xy

x^2 = 3y^2 + 2xy

 

So we're looking for xy, and we could solve for it, but let's just say x = 1 for simplicity.

1^2 = 3*y^2 + 2(1)y

1 = 3y^2 + 2y. 

y = 1/3. 

So y/x = 1/3/1 = 1/3. 

 

I hope this helped. :)))

=^._.^=

 

here's link

https://web2.0calc.com/questions/right-triangle_21

 Jul 4, 2022
 #2
avatar+124676 
+1

Taking this from

 

x^2 =  3y^2 + 2xy

 

x^2  - 2xy  - 3y^2  = 0

 

(x - 3y) ( x + y) = 0

 

x + y = 0    not possible

 

x - 3y = 0

 

x = 3y

 

y / x =   1 /  3

 

cool cool cool

 Jul 4, 2022

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