Question

The breadth of a rectangle is $10\%$ of its perimeter. If the length of the rectangle is $12$ cm longer than its breadth, find the area of the rectangle.

• A. $36c{m}^2$
• B. $400c{m}^2$
• C. $64c{m}^2$
• D. $256c{m}^2$

Answer 1

The correct option is C $64c{m}^2$

Let the breadth of rectangle is $y$ cm

Then length of rectangle $=y+12$ cm ....Given

So perimeter of rectangle $=2(y+12+y)=4y+24$

But perimeter of rectangle $=$ $y\times \frac{10}{100}$ cm ....( Given that perimeter of rectangle is $10\%$ of breadth)

So, $4y+24=\frac{y}{10}$

$\Rightarrow 4y-10y=-24$

$\Rightarrow y=4.00$ cm

Thus, length of rectangle will be $y+12=4+12=16$ cm

Therefore, area of the rectangle is $l\times b=4\times 16=64c{m}^2$