Question

Solve the following problems:

The length of a rectangle is three times its breadth. If the perimeter is $88$cm, find the length and breadth.

Answer 1

Finding the length and breadth of the rectangle.

Given: The length of a rectangle is three times its breadth and the perimeter $=88$cm

Let the breadth of the given rectangle be $\mathrm{x}$ cm.

$\therefore$ Length of the rectangle is $3\mathrm{x}$ cm.

We know that the perimeter of rectangle $=2(\mathrm{Length}+\mathrm{breadth})$

$$\begin{gathered} \Rightarrow 88=2(3\mathrm{x}+\mathrm{x}) \\ \Rightarrow 2(3\mathrm{x}+\mathrm{x})=88 \\ \Rightarrow 2\left(4\mathrm{x}\right)=88 \\ \Rightarrow 8\mathrm{x}=88 \\ \Rightarrow \frac{8\mathrm{x}}{8}=\frac{88}{8} \\ \therefore \mathrm{x}=11 \end{gathered}$$

So, length of the rectangle $=3\mathrm{x}=3\times 11=33\mathrm{cm}$

Hence, the length and breadth of the given rectangle are $33\mathrm{and}11$ respectively.