SOLUTION: The lengths of the three sides of a right triangle are represented by consecutive whole numbers. Find the lengths of the three sides.

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Question 154120This question is from textbook Intermediate Algebra
: The lengths of the three sides of a right triangle are represented by consecutive whole numbers. Find the lengths of the three sides. This question is from textbook Intermediate Algebra

Answer by jojo14344(1513) About Me  (Show Source):
You can put this solution on YOUR website!
Remember:
adjacent=a=x
opposite=o=x%2B1
hypotenuse=h=x%2B2
consecutive numbers system%28x%2Cx%2B1%2Cx%2B2%29
By Pyth theorem:
h%5E2=a%5E2%2Bo%5E2 ------------------> working eqn
%28x%2B2%29%5E2=x%5E2%2B%28x%2B1%29%5E2
x%5E2%2B4x%2B4=x%5E2%2Bx%5E2%2B2x%2B1
2x%5E2%2B2x%2B1-x%5E2-4x-4=0
x%5E2-2x-3=0
By Quadratic : a=1, b=-2, & c=-3
x=%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F2a
x=%28-%28-2%29%2B-sqrt%28-2%5E2-4%2A1%2A-3%29%29%2F%282%2A1%29
x=%282%2B-sqrt%284%2B12%29%29%2F2
x=%282%2B-sqrt%2816%29%29%2F2
x=%282%2B-4%29%2F2
2 VALUES:
x=%282%2B4%29%2F2=6%2F2=3 -------> USED
x=%282-4%29%2F2=-2%2F2=-1-------> DON'T USED
So the sides:
adjacent=3
opposite=3%2B1=4
hypotenuse=3%2B2=5
In doubt? go back working eqn:
5%5E2=3%5E2%2B4%5E2
25=9%2B16
25=25
Thank you,
Jojo