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24 August, 02:04

If the perimeter of A rectangle is 70" in and the length is 11" in more than its width find the area of the rectangle

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  1. 24 August, 05:26
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    First, write an equation system based on the problem

    An equation for "the perimeter of a rectangle is 70 in" can be written as following

    ∴ 2l + 2w = 70 (first equation)

    An equation for "the length is 11 in more than its width" can be written as following

    ∴ l = w + 11 (second equation)

    Second, solve the equation by substitution method o find the dimension of the rectangle.

    Substitute/plug l as (w+11) into the first equation

    2l + 2w = 70

    2 (w + 11) + 2w = 70

    2w + 22 + 2w = 70

    4w + 22 = 70

    4w = 70 - 22

    4w = 48

    w = 48/4

    w = 12

    The width of the rectangle is 12 in

    Substitute w with 12 to the second equation

    l = w + 11

    l = 12 + 11

    l = 23

    The length of the rectangle is 23 in

    Third, find the area of the rectangle

    a = l * w

    a = 23 * 12

    a = 276

    The area of the rectangle is 276 in²
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