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12 January, 22:04

The height of a triangle is 6 feet greater than the base the area of the triangle is 108 square feet find the length of the base and the height of the triangle

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  1. 13 January, 00:36
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    Answer: the length of the base is 12 feet and the height is 18 feet.

    Step-by-step explanation:

    We would assume that the triangle is a right angle triangle. The formula for determining the area of a triangle is expressed as

    Area = 1/2 * base * height

    Let b represent the base of the triangle.

    The height of the triangle is 6 feet greater than the base. It means that the height is (b + 6) feet.

    If the area of the triangle is 108 square feet, it means that

    108 = 1/2 * b (b + 6)

    Cross multiplying by 2, it becomes

    216 = b² + 6b

    b² + 6b - 216 = 0

    b² + 18b - 12b - 216 = 0

    b (b + 18) - 12 (b + 18) = 0

    b - 12 = 0 or b + 18 = 0

    b = 12 or b = - 18

    Since the base cannot be negative, then b = 12 feet

    Height = b + 6 = 12 + 6 = 18 feet
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