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The longer leg of a right triangle is 8 more than the shorter leg.   The hypotenuse is 6 more than the longer leg.   Find all three sides.

 Apr 23, 2021
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Let  the  longer  leg   =  x

The shorter leg  =  x - 8

The hypotenuse  =  x  + 6

 

By Pythagoras

 

(x - 8)^2  + x^2  = ( x + 6)^2      simplify

 

x^2 - 16x + 64  + x^2  = x^2  + 12x +  36

 

2x^2  - 16x  +  64  =  x^2  + 12x +  36

 

x^2 - 28x + 28 =  0

 

Using the  Quad Formla 

 

x =   ( 28  ±  sqrt  [  28^2  -  4*28]  )  /  2

 

x ≈  1.04  reject

 

x ≈   27   =  the longer leg

 

x - 8  ≈  19 = the shorter leg

 

x + 6  ≈ 33  the hypotenuse

 

 

cool cool cool

 Apr 23, 2021

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