rectangle

**sri340** · May 12th 2010, 04:35 PM

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

**Soroban** · May 12th 2010, 05:53 PM

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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