SOLUTION: Find the lengths of the three sides of the right triangle if the two legs measure x feet, (x+14) feet, respectively, and the hypotenuse measure (x+16) feet.

Question 933531: Find the lengths of the three sides of the right triangle if the two legs measure x feet, (x+14) feet, respectively, and the hypotenuse measure (x+16) feet.
Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!
x^2+(x+14)^2 = (x+16)^2 by Pythagoras theorem
x^2+x^2+28x+196 = x^2+32x+256
simplify
x^2-4x-60=0
x^2-10x+6x-60=0
x(x-10)+6(x-10)=0
(x-6)(x-10)=0
x= 6 OR 10
check which is applicable
x=6
x+14=20
x+16=22
6^2+20^2=36+400 = 436
22^2= 441
x=6 is not applicable
substitute the value of x
10^2+24^2=676
26^2=676
so the sides are 10,24 & 26
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