Thread: 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

Hello, sri340!

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

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

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

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

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


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

. . $\displaystyle \begin{array}{ccc}\text{Length} & \text{Width} & \text{Perimeter} \\ \hline
10 & 1 & 22 \\ 5 & 2 & 14 \end{array}$


The largest perimeter is 22 cm . (A)