Question

The perimeter of a rectangle is $130\mathrm{cm}$.

If the breadth of the rectangle is $30\mathrm{cm}$, find its length. Also, find the area of the rectangle.

Answer 1

Step 1. Calculate the length of the rectangle.

Let us consider that length and breadth of the rectangles are $l$ and $b$respectively.

$$\begin{gathered} \mathrm{Perimeter}=130 \\ \Rightarrow 2(l+b)=130 \\ \Rightarrow l+b=65 \\ \Rightarrow l+30=65\left[\because b=30\mathrm{cm}\right] \\ \Rightarrow l=65-30 \\ \Rightarrow l=35\mathrm{cm} \end{gathered}$$

Thus, the length of the rectangle is $35\mathrm{cm}$.

Step 2. Calculate the area of the rectangle.

$\begin{array}{rcl}\mathrm{Area}& =& l\times b\\ & =& 35\times 30\\ & =& 1050{\mathrm{cm}}^2\end{array}$

Hence, the length is $35\mathrm{cm}$ and the area of the rectangle is $1050{\mathrm{cm}}^2$.