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March 30, 2017

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The shorter leg of a right triangle is 14 feet shorter than the longer leg. The hypotenuse is 26 feet. How long is each leg?

  • Math - ,

    (X-14)^2+X^2 = 26^2
    solve for x and x-14

  • Math - ,

    a=shorter leg
    b=longer leg
    c=hypotenuse

    a=b-14

    c^2=a^2+b^2
    26^2=(b-14)^2+b^2
    676=b^2-2*b*14+14^2+b^2
    676=2b^2-28b+196
    676-196=2(b^2-14b)
    480=2(b^2-14b) Divide with 2
    240=b^2-14b
    b^2-14b=240
    b^2-14b+7^2=240+7^2

    Becouse: (b-7)^2=b^2-14b+7^2

    (b-7)^2=240+49
    (b-7)^2=289
    b-7=sqroot(289)

    You have two solutions:
    b-7=17 and
    b-7=-17

    Becouse sqroot(289)=+/- 17

    First solution: b-7=17
    b=17+7=24

    Second solution:
    b-7=-17
    b=17+7=-10

    leg of triangle can not be negative number so:
    b=24
    a=b-14=24-14=10

    a=10 b=24

    c=sqroot(a^2+b^2)
    c=sqroot(10^2+24^2)
    c=sqroot(100+576)
    c=sqroot(676)

    c=26

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