SOLUTION: The sides of a right triangle are x, x+17, and x+18 units long. what is the length of the hypotenuse

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Question 281536: The sides of a right triangle are x, x+17, and x+18 units long. what is the length of the hypotenuse
Found 2 solutions by richwmiller, JBarnum:
Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
the longest side is the hypotenuse x+18
x^2+(x+17)^2=(x+18)^2
x=7
x+18=25
7^2+24^2=25^2
49+576=625
hypotenuse is 25


Answer by JBarnum(2146) About Me  (Show Source):
You can put this solution on YOUR website!
what we know:
3sides with x, x+17, and x+18
x+18 side is the largest side so thats the hypotnuse
A%5E2%2BB%5E2=C%5E2 A=x B=x+17 C=x+18
use substitution and solve for x
x%5E2%2B%28x%2B17%29%5E2=%28x%2B18%29%5E2
x%5E2%2B%28x%5E2%2B34x%2B289%29=%28x%5E2%2B36x%2B324%29put all on 1 side set = to 0
x%5E2%2Bx%5E2%2B34x%2B289-x%5E2-36x-324=0 reorganize
x%5E2%2Bx%5E2-x%5E2%2B34x-36x%2B289-324=0 add like terms
x%5E2-2x-35=0 -7 and +5 multiply to get -35 and add to get -2
x%2B5=0x-7=0
x=-5x=7
since the side cant be - then x=7
A=7
B=24
C=25
25=hypotenuse length