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19 March, 14:11

A rectangular bathroom mirror has a perimeter of 22 feet. Its area is 30 square feet. What are the dimensions of the mirror?

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  1. 19 March, 16:25
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    6 feet long and 5 feet wide.

    Explanation:

    Given that the formula for area is:

    A=Length x Width

    And perimeter is:

    P = 2L + 2W

    We know area is 30 and perimeter is 22, so our equations are:

    30 = L * W

    22 = 2L + 2W

    To solve as a system of equations, lets isolate L on the second equation.

    22 = 2L + 2W

    22 - 2W = 2L

    Divide both sides by 2

    11 - W = L

    Inserting it into the first equation

    30 = (11 - W) W

    30 = 11W - W²

    This looks like a quadratic, so let's bring everything to the left side and factor.

    W² - 11W + 30 = 0

    (W - 6) (W - 5) = 0

    W = 6 or W = 5

    Insert both of these into 30 = L*W to find L

    30 = 6L

    L = 5 when W = 6

    or 30 = 5L

    L = 6 when W = 5

    Hence, the mirror is 6 feet long and 5 feet wide.
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