Question

In a rectangle, length is twice the breadth. If the length of a rectangle is increased by 20% and its breadth is increased by 10%. The percentage increase in its perimeter will be :

Answer 1

Dear Student,

Let the length and breadth of the rectangle be $l$ and $b$ respectively. It is given that length is twice its breadth so $l=2b$
Then, perimeter$=2\left(2b+b\right)=2\times 3b=6b$.
Now, it is given that length is increased by 20%. So, new length $=l+\frac{20}{100}l=\frac{120}{100}l=1.2l=1.2\times 2b=2.4b$.
Also, breadth is increased by 10%. So, new breadth $=b+\frac{10}{100}b=\frac{110}{100}b=1.1b$.
Therefore, new perimeter $=2\left(2.4b+1.1b\right)=2\times 3.5b=7b$.
Percentage increase in perimeter is given as

$$\begin{gathered} =\frac{Newperimeter-Originialperimeter}{Originialperimeter}\times 100\% \\ =\frac{7b-6b}{6b}\times 100\% \\ =\frac{b}{6b}\times 100\% \\ =\frac{100}{6}\% \\ =16.67\% \end{gathered}$$
Regards,