Quandaries & Queries - Math Central

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Quandaries & Queries

Brad, a parent:

I am having a problem coming up with a formula for my son's eighth grade math problem.
We have found the answer by guess and check but have a mental block on the equation.
Any help would be appreciated.
The problem is: A right triangle has sides whose lengths in feet are consecutive even intergers. Determine the length of each side.

Thanks

Hi Brad,

Each consecutive even integer is separate by 2 so the sides would be n, n+2 and n+4. Since the hypotenuse is the longest side, I know that will be n+4.

We can use the Pythagorean Theorem to solve for n. So then
n²+(n+2)²=(n+4)²
n²+n²+4n+4=n²+8n+16
2n²+4n+4=n²+8n+16
n²-4n+12=0
(n-6)(n+2)=0
n=6 or n=-2
Since the side of the triangle cannot be negative, n=6. So the length of the sides are 6, 8 & 10.

Hope this helps. If your son has not learned factoring or polynomial multiplication in school yet, guess and check might be the best option.

Janice

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