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3 June, 17:02

the height of a triangle is 4 less than it's base. The area of the triangle is 30 square inches. Find the length of the base to the nearest inch

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  1. 3 June, 17:52
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    10 inches

    Step-by-step explanation:

    The formula for the triangle area is the following:

    A = b * h / 2

    Where b is the length of the base side and h is the height.

    So, as the height is 4 less than the base, we have that:

    h = b - 4

    Using this value in the area equation, we have that:

    A = b * (b - 4) / 2

    30 = (b^2 - 4b) / 2

    b^2 - 4b = 60

    b^2 - 4b - 60 = 0

    Using Bhaskara's formula to solve the quadratic equation, we have:

    Delta = 4^2 + 4*60 = 256

    sqrt (Delta) = 16

    b1 = (4 + 16) / 2 = 10

    b2 = (4 - 16) / 2 = - 6 (negative value does not fit for this problem)

    So the length of the base is 10 inches.
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