Question

The length of a rectangle is three times its breadth. The perimeter of that rectangle is $40\text{cm}$.

Find its length and width.

Answer 1

The perimeter $P$ of the rectangle with length $l$ and width $w$ is given by, $P=2\left(l+w\right)$.

Let the width of the rectangle be $x\text{cm}$, then the length of the rectangle will be $3x\text{cm}$.

Step 1: Substitute $l=3x$, $w=x$ and $P=40$ into $P=2\left(l+w\right)$ and solve for $x$.

$$\begin{gathered} 40=2\left(3x+x\right) \\ 40=2\left(4x\right) \\ 40=8x \end{gathered}$$

Step 2: Divide both sides of the equation by $8$ and solve for $x$.

$\begin{array}{rcl}\frac{40}{8}& =& \frac{8x}{8}\\ x& =& 5\end{array}$

Step 3: Substitute $x=5$ into $l=3x$ and $w=x$ to find the length and width of the rectangle.

$\begin{array}{rcl}l& =& 3\left(5\right)\\ & =& 15\text{cm}\end{array}$;

$w=5\text{cm}$

Hence, the length of the rectangle is $15\text{cm}$ and the width of the rectangle is $5\text{cm}$.