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5 March, 14:59

The area of the numbered triangle on a shuffle board court is 27 ft^2.

Its height is 3 feet more than the length of the base. Find the length of the base and the height.

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  1. 5 March, 17:14
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    Area of a triangle = 1/2 * base * height

    Its height is 3 feet more than the base.

    Let's substitute "b + 3" for the height so we only have one variable to solve for.

    27 = 1/2 * b * (b + 3)

    Let's multiply by 2 to get rid of the 1/2.

    54 = b * (b + 3)

    Distribute.

    54 = b² + 3b

    Multiple ways to solve this: You could guess and check ...

    If b = 5 then we'd have 25 + 15 = 40

    If b = 6 then we'd have 36 + 18 = 54 - - > base = 6 feet

    Then, putting b = 6 into our equation with the height ...

    27 = 1/2 * b * h

    54 = 6 * h

    height = 9 feet

    Or you could factor and solve the quadratic. (Algebra I concept)

    b² + 3b - 54 = 0

    We want two numbers that multiply to equal - 54 and add to equal 3.

    -54 = - 6 * 9

    3 = - 6 + 9

    Split the milddle ...

    b² - 6b + 9b - 54 = 0

    Factor the first and last two pairs of terms.

    b (b-6) + 9 (b-6)

    (9+b) (b-6) = 0

    Any value of b which causes either factor to equal 0 is a solution.

    9 + b = 0 or b - 6 = 0

    b = - 9 or b = 6

    Since b is a side length, it can be only positive.

    base = 6 feet

    Then you wouldl use that b = 6 in an earlier equation to find h = 9.
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