Question

The perimeter of a rectangle is numerically equal to the area of rectangle. If width of rectangle is $2\frac{3}{4}$cm, then its length is _________.

• A. $\frac{11}{3}$cm
• B. $\frac{22}{3}$cm
• C. $11$cm
• D. $10$cm

Answer 1

The correct option is B $\frac{22}{3}$cm

Let sides of rectangle are $a$ and $b$

$a$ $=$ length

$b$ $=$ width

We know perimeter $=2(a+b)$

Area $=a\times b$

Here width $=\frac{11}{4}=b$

$2(a+b)=a\times b$

$\Rightarrow 2(a+\frac{11}{4})=a\times \frac{11}{4}$

$\Rightarrow (2-\frac{11}{4})a=-\frac{11}{2}$

$\Rightarrow -\frac{3}{4}a=-\frac{11}{2}$

$\Rightarrow a=\frac{22}{3}$