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2 January, 09:34

The perimeter of the patio is 64 feet. The width of the patio is (x+2) feet and the length of the patio is (x+6) feet. What are the dimensions of the patio?

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  1. 2 January, 13:13
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    The formula for the perimeter is P = 2w + 2l, where w is the width and l is the length. It is given that the width = (x+2) and the length = (x+6). Therefore, we can make this equation:

    P = 2w + 2l

    64 = 2 (x+2) + 2 (x+6) ⇒ Distributive property

    ⇒ 64 = 2x + 4 + 2x + 12 ⇒ Combine like terms

    ⇒ 64 = 4x + 16 ⇒ Subtract 16 from both sides

    ⇒ 48 = 4x ⇒ Divide both sides by 4

    ⇒ x = 12

    Then, we use x = 12 and substitute it in to find the length and width

    Width = (x+2) = (12+2) = 14

    Length = (x+6) = (12+6) = 18

    The dimensions of the patio is 14 by 18
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