Question

The ratio of the length and breadth of a rectangle is $5:2$ respectively. The respective ratio of its perimeter and area is $1:3$ (irrespective of the unit). What is the length of the rectangle?

• A. $27$ units
• B. $32$ units
• C. $21$ units
• D. $84$ units

Answer 1

Answer: (C)

$21$ units

Let length $=5x$ and breadth$=2x$

Area of rectangle$=5x\times 2x=10x^2$

Perimeter of rectangle$=2(l+b)=2\times (5x+2x)=14x$

Now, $\frac{P}{A}=\frac{1}{3}\Rightarrow \frac{14x}{10x^2}=\frac{1}{3}\Rightarrow x=4.2$

$\therefore$Length of rectangle$=5\times 4.2=21$ units.