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3 January, 12:41

An orange triangular warning sign by the side of the road has an area of 266 square inches. The base of the sign is 9 inches longer than the altitude. Find the measurements of the base and altitude.

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  1. 3 January, 12:56
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    Answer: the base is 28 inches. The altitude is 9 inches

    Step-by-step explanation:

    Let h represent the altitude of the sign.

    Let b represent the length if the base of the sign.

    The warning sign is triangular in shape.

    The formula for determining the area of a triangle is expressed as

    Area = 1/2bh

    The base of the sign is 9 inches longer than the altitude. This means that

    b = h + 9

    If the area of the sign is 266 square inches, it means that

    266 = 1/2 * h (h + 9)

    266 * 2 = h (h + 9)

    532 = h² + 9h

    h² + 9h - 532 = 0

    h² + 28h - 19h - 532 = 0

    h (h + 28) - 19 (h + 28) = 0

    h (h + 28) - 19 (h + 28) = 0

    (h + 28) (h - 19) = 0

    h = 19 or h = - 28

    Since the height cannot be negative, then h = 19

    b = h + 9 = 10 + 9

    b = 28
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