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Math Help - rectangle

  1. #1
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    rectangle

    The length, L, of a rectangle is increased by 50% and the width, W, is doubled to form a larger rectangle with an area of 30 cm2. What is the largest possible perimeter of the larger rectangle if L and W are integers with L > W?

    (A) 22 cm (B) 23 cm (C) 26 cm (D) 34 cm (E) 43 cm
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  2. #2
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    Hello, sri340!

    The length L of a rectangle is increased by 50% and the width W
    is doubled to form a larger rectangle with an area of 30 cm².

    What is the largest possible perimeter of the larger rectangle
    if L and W are integers with L > W ?

    . . \text{(A) 22 cm} \quad\text{(B) 23 cm}\quad\text{(C) 26 cm} \quad \text{(D) 34 cm} \quad \text{(E) 43 cm}

    The new rectangle has length \tfrac{3}{2}L and width 2W.

    Its area is 30 cm²: . \left(\tfrac{3}{2}L\right)(2W) \:=\:30 \quad\Rightarrow\quad LW \:=\:10


    Since L and W are integers with L > W
    . . there are only two possible cases:

    . . \begin{array}{ccc}\text{Length} & \text{Width} & \text{Perimeter} \\ \hline<br />
10 & 1 & 22 \\ 5 & 2 & 14 \end{array}


    The largest perimeter is 22 cm . (A)

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