math

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2. One side of a right triangle is 12.5 ft. The perimeter is 38.7 ft. What is the length of the hypotenuse and the other unknown side?

  • math -

    let x = hypotenuse
    let y = the length of the other leg
    we have two equations, two unknowns here.
    recall that perimeter of a triangle is just,
    P = a + b + c
    substituting,
    38.7 = x + y + 12.5
    x + y = 38.7 - 12.5
    x + y = 26.2
    x = 26.2 - y : : equation (1)

    recall that for any right triangle, we can solve for hypotenuse using the Pythagorean theorem:
    c^2 = a^2 + b^2
    substituting,
    y^2 = x^2 + 12.5^2
    y^2 = x^2 + 156.25 : equation (2)
    now, we substitute eqn (1) to eqn (2):
    y^2 = (26.2 - y)^2 + 156.25
    y^2 = 686.44 - 52.4y + y^2 + 156.25
    y^2 - y^2 + 52.4y = 842.69
    52.4y = 842.69
    y = 16.08 ft (hypotenuse)
    x = 26.2 - y = 10.12 ft (other leg)

    hope this helps~ :)

  • math -

    P = Perimeter

    a = First side = 12.5 ft

    b = Second side

    c = Hypotenuse


    c = sqrt ( a ^ 2 + b ^ 2 )

    c = sqrt ( 156.25 + b ^ 2 )


    P = a + b + c = 38.7

    12.5 + b + sqrt ( 156.25 + b ^ 2 ) = 38.7

    b + sqrt ( 156.25 + b ^ 2 ) = 38.7 -12.5

    b + sqrt ( 156.25 + b ^ 2 ) = 26.2

    sqrt ( 156.25 + b ^ 2 ) = 26.2 - b Square both sides

    156.25 + b ^ 2 = ( 26.2 - b ) ^ 2

    156.25 + b ^ 2 = 26.2 ^ 2 - 2 * 26.2 * b + b ^ 2

    156.25 + b ^ 2 = 686.44 - 52.4 b + b ^ 2

    b ^ 2 + 52.4 b - b ^ 2 = 686.44 - 156.25

    52.4 b = 530.19 Divide both sides with 52.4

    b = 530.19 / 52.4

    b = 10.118129771 ft


    c = sqrt ( a ^ 2 + b ^ 2 )

    c = sqrt ( 12.5 ^ 2 + 10.118129771
    ^ 2 )

    c = sqrt ( 156.25 + 102.37655 )

    c = sqrt ( 258.62655 )

    c = 16.08187 ft

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