Question

Question 96

Solve the following:

The perimeter of a rectangle is 240cm. If its length is is increased by 10% and its breadth is decreased by 20%, then we get the same perimeter. Find the length and breadth of the rectangle.

Answer 1

Given, perimeter of rectangle =240m
$\Rightarrow 2\times (Length+Breadth)$=240 cm
$\Rightarrow$ Length+Breadth=120 cm
Let the length of rectangle be x cm.
Then, the breadth of rectangle =(120-x) cm
$\therefore$ New length of rectangle =x+10% of x=x+ $\frac{10}{100}\times x=\frac{110}{100}xcm$
$(120-x)-\frac{20}{100}\times (120-x)(120-x)(1-\frac{20}{100})=\frac{80}{100}(120-x)cm$
It is given that, perimeter of new rectangle is 240 cm.
According to the question,
$2\times (Newlength+Newbreadth)=240$
$\Rightarrow 2\times [\frac{110x}{100}+\frac{80}{100}(120-x\left)\right]=240\Rightarrow \frac{110x+9600-80x}{100}=\frac{240}{2}\Rightarrow 30x+9600=\frac{240}{2}\times 100\Rightarrow 30x+9600=12000\Rightarrow 30x=12000-9600\Rightarrow 30x=2400\Rightarrow x=\frac{2400}{30}=80$
Hence, length of rectangle=80cm
and breadth of rectangle=120-80=40cm.