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The longer leg of a right triangle is 8 more than the shorter leg.   The hypotenuse is 10 more than the longer leg.   Find all three sides.

 Dec 1, 2020
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Let the shorter leg  = x

The longer leg  x + 8

The hypotenuse   x + 8 + 10   =  x + 18

 

By rhe Pythagorean Theorem, we have

 

x^2  +  ( x + 8)^2  =  (x + 18)^2     simplify

 

x^2  + x^2 + 16x  + 64  =  x^2  + 36x + 324

 

2x^2 + 16x  +  64  =  x^2  + 36x + 324

 

x^2 - 20x  - 260  =  0      complete the square on x

 

x^2 - 10x + 100  =  260 + 100

 

(x - 10)^2 =  360       take the positive roor

 

x - 10    = sqrt (360)

 

x - 10  = 6sqrt (10)

 

x  =  6sqrt (10)  + 10   = shorter leg

x + 8  =  6sqrt (10) + 18  = longer leg

x + 18 = 6sqrt (10) + 28    = hypotenuse

 

cool cool cool

 Dec 1, 2020

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