Question 198392: Quadratic Equations
13. The three sides of a right triangle are consecutive even integers. What is the length of each side?
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Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! Quadratic Equations
13. The three sides of a right triangle are consecutive even integers.
What is the length of each side?
:
Let side 1 = x,
Let side 2 = (x+2)
Hypotenuse = (x+4)
:
x^2 + (x+2)^2 = (x+4)^2
FOIL
x^2 + x^2 + 4x + 4 = x^2 + 8x + 16
Combine on the left
x^2 + x^2 - x^2 + 4x - 8x + 4 - 16 = 0
A quadratic equation
x^2 - 4x - 12 = 0
Factors to:
(x-6)(x+2) = 0
The positive solution
x = 6 is side 1
6 + 2 = 8 is side 2
6 + 4 = 10 is the hypotenuse
:
6, 8, 10 consecutive even integers
;
;
Check solution
6^2 + 8^2 = 10^2
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