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22 December, 17:02

The sides of a rectangle are in a 3:4 ratio. What is the length of the shorter sides of the rectangle if it's perimeter is 42cm

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  1. 22 December, 17:24
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    The perimeter of any rectangle is P = 2L + 2W. It is customary to make the length (L) the longest side. That being said, the object is to set up a proportion and substitute that into the Perimeter formula.

    Givens

    P = 42 cm

    W / L = 3/4

    Set up the two equations from the givens.

    P = 2L + 2W = 42

    W = 3/4 L

    Step One

    Substitute the second equation into the first.

    2L + 2 (3/4) L = 42 Make an improper fraction of second term on the left.

    2L + 6/4 L = 42 Reduce the fraction

    2L + 3/2 L = 42 Multiply through by 2

    4L + 3L = 84 Combine like terms.

    7L = 84 Divide by 7

    L = 84/7

    L = 12

    Step 2

    Find the Width.

    3/4 = W/12 Cross multiply

    4W = 36 Divide by 4

    W = 36/4

    W = 9

    Check

    P = 2L + 2W

    2L + 2W = 42

    2*12 + 2*9 = ? 42

    24 + 18 = ? 42

    42 = 42
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