Question

Solve the following problems:

The length of a rectangle is $8\mathrm{cm}$ more than twice its breadth. If its perimeter is $76\mathrm{cm}$, find the length and breadth.

Answer 1

Given, that the length of a rectangle is $8\mathrm{cm}$ more than twice its breadth, and the perimeter rectangle is $76\mathrm{cm}$

Let the breadth of the given rectangle is $\mathrm{x}\mathit{}\mathrm{cm}$

So, the length of a rectangle is $(2\mathrm{x}+8)\mathit{}\mathrm{cm}$.

According to the given condition,

$\mathrm{Perimeter}\mathrm{of}\mathrm{rectangle}=2(\mathrm{Length}+\mathrm{Breadth})$

$$\begin{gathered} \Rightarrow 76=2\left[(2\mathrm{x}+8)+\mathrm{x}\right] \\ \Rightarrow 76=2(2\mathrm{x}+8+\mathrm{x}) \\ \Rightarrow 76=2(3\mathrm{x}+8) \\ \Rightarrow 2\times 3\mathrm{x}+2\times 8=76[\mathrm{Distributive}\mathrm{property}] \\ \Rightarrow 6\mathrm{x}+16=76 \\ \Rightarrow 6\mathrm{x}=76-16 \\ \Rightarrow 6\mathrm{x}=60 \\ \Rightarrow \mathrm{x}=\frac{60}{6} \\ \therefore \mathrm{x}=10\mathrm{cm} \end{gathered}$$

So, the length of a rectangle

$$\begin{gathered} =(2\mathrm{x}+8) \\ =2\times 10+8 \\ =20+8 \\ =28cm \end{gathered}$$.

Hence, the length and breadth of the given rectangle are $10\mathrm{cm}\mathrm{and}28\mathrm{cm}$respectively.