Question

Solve the following problems:

The perimeter of a rectangle is $68$cm. If its breadth is $4$cm less than its length, find the length and breadth.

Answer 1

Given: Perimeter $=68$cm and breadth $=4$ cm less than its length.

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

$\therefore$ Breadth of the rectangle is $(\mathrm{x}-4)$cm

Now, Perimeter of rectangle $=2(\mathrm{Length}+\mathrm{breadth})$

$$\begin{gathered} \Rightarrow 68=2(\mathrm{x}+(\mathrm{x}-4\left)\right) \\ \Rightarrow 2(2\mathrm{x}-4)=68[\mathrm{Simplifying}\mathrm{and}\mathrm{rearranging}] \\ \Rightarrow 4\mathrm{x}-8=68 \\ \Rightarrow 4\mathrm{x}-8+8=68+8[\mathrm{Adding}8\mathrm{to}\mathrm{both}\mathrm{sides}] \\ \Rightarrow 4\mathrm{x}=76 \\ \Rightarrow \frac{4x}{4}=\frac{76}{4}[\mathrm{Dividng}\mathrm{both}\mathrm{sides}\mathrm{by}4] \\ \therefore \mathrm{x}=19 \end{gathered}$$

So, the breadth of the rectangleis

$$\begin{gathered} =\mathrm{x}-4 \\ =19-4 \\ =15\mathrm{cm} \end{gathered}$$

Hence, the length and breadth of the given rectangle are $19\mathrm{and}15$ respectively.