Question

The length and breadth of a rectangle are in the ratio $3:2$ respectively. If the sides of the rectangle are extended on each side by $1m$, the ratio of length to breadth becomes $10:7$. Find the area of the original rectangle in square metres.

• A. $23m^2$
• B. $11m^2$
• C. $54m^2$
• D. $10m^2$

Answer 1

Answer: (C)

$54m^2$

Given, the length and breadth of a rectangle are in the ratio $3:2$ respectively.

Then let the length and breadth of the rectangle be $3x,2x$ respectively.

If the sides of the rectangle are extended on each side by $1$ m then length and breadth will be $3x+1$ m and $2x+1$ m.

According to the problem,

$\frac{3x+1}{2x+1}=\frac{10}{7}$

or, $20x+10=21x+7$

or, $x=3$.

So length and breadth are $9,6$ m respectively.

Now area of the rectangle be $9\times 6=54$ m${}^2$.