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# Algebra II word problem?

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

thank you so much.

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- whitesox09Lv 71 decade agoFavorite Answer
3 4 5

x = the smallest length [leg 1]

y = x+1 [leg 2]

z = x+2 [hypotenuse]

By pythagorean theorem

x^2 + y^2 = z^2

(x)^2 + (x+1)^2 = (x+2)^2

x^2 + x^2 +2x + 1 = x^2 + 4x + 4

2x^2 + 2x + 1 = x^2 + 4x + 4

x^2 - 2x - 3 = 0

(x+1)(x-3)=0

x = -1 (this is extraneous because length is always positive)

x = 3

y = x + 1 = 4

z = x + 2 = 5

- yupchageeLv 71 decade ago
3, 4, & 5. I just know this. You can find it from the Pythagorean theorem.

n²+(n+1)²=(n+2)²

n²+n²+2n+1=n²+4n+4 subtract n²+4n+4 from each side

n²-2n-3=0

(n-3)(n+1)=0 since n>0

n-3=0

n=3

n+1=4

n+2=5

3, 4, 5 right triangle.

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