jaz
Lv 5
jaz asked in Science & MathematicsMathematics · 1 decade ago

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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  • 1 decade ago
    Favorite 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

  • 1 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.

  • 1 decade ago

    3,4,5

  • Ashley
    Lv 4
    1 decade ago

    3,4,5

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  • 1 decade ago

    3,4,5

  • 1 decade ago

    3,4,5

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