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23 September, 13:32

Jack has a rectangular patio with a length that is one foot less than twice its width. His neighbor Ron's patio has the same width but a length that is 5 feet more than its width. If Jack's patio is 120 square feet and Ron's patio is 104 square feet, how many square feet longer is Jack's patio than Ron's?

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  1. 23 September, 15:59
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    difference in area = 16 ft²

    if you use 8 the difference in length between Jack patio and his neighbor patio will be will be 15 - 13 = 2 ft

    if you use 13 the difference i length will be 25 - 18 = 7 ft

    Step-by-step explanation:

    Jacks rectangular patio

    width = a

    length = 2a - 1

    area = lw

    where

    l = length

    w = width

    area = 120 ft²

    a (2a - 1)

    2a² - a - 120 = 0

    (a - 8) (2a + 15)

    a = 8 or - 15/2

    Ron's rectangular patio

    width = a

    length = a + 5

    area = lw

    area = 104 ft²

    a (a + 5) = 104

    a² + 5a - 104 = 0

    (a + 8) (a - 13)

    a = - 8 or 13

    How many square feet longer is jack patio longer than Ron's patio is the difference in their area. Therefore,

    120 - 104 = 16 ft²

    The value 8 or 13 can be used for a since the width a have to be the same.

    if you use 8 the difference in length between Jack patio and his neighbor patio will be will be 15 - 13 = 2 ft

    if you use 13 the difference i length will be 25 - 18 = 7 ft
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