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4 November, 13:12

The area of a room is 425 square feet. The length is (x+10) and the width is (x+2) feet. Find the dimensions of the room.

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  1. 4 November, 13:23
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    length = 25 feet and width = 17 feet

    Step-by-step explanation:

    area (A) = length * width, hence

    A = (x + 10) (x + 2) ← expand factors

    = x² + 12x + 20

    given A = 425, then

    x² + 12x + 20 = 425 (subtract 425 from both sides)

    x² + 12x - 405 = 0 ← in standard form

    (x + 27) (x - 15) = 0 ← in factored form

    equate each factor to zero and solve for x

    x + 27 = 0 ⇒ x = - 27

    x - 15 = 0 ⇒ x = 15

    but x > 0 ⇒ x = 15, therefore

    length = 15 + 10 = 25 feet and width = 15 + 2 = 17 feet
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