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. $7\frac{1}{8}$cm
• B. $7\frac{1}{3}$cm
• C. $5\frac{1}{3}$cm
• D. None of these

Answer 1

The correct option is B $7\frac{1}{3}$cm

Given:- perimeter of rectangle = area of rectangle

$2(l+b)=lb..\left(1\right)$

if $b=2\times \frac{3}{4}=\frac{11}{4}cm$

$l=?$

$2(l+\frac{11}{4})=l\left(\frac{11}{4}\right)$

$2l-\left(\frac{11l}{4}\right)=-\frac{11}{2}$

$\Rightarrow \frac{3l}{4}=\frac{11}{2}\Rightarrow l=\frac{22}{3}=7\frac{1}{3}cm$

$\therefore$ if breadth $=2\frac{3}{4}cm$ than length = $7\frac{1}{3}cm$