Question

The perimeter of rectangle and a square are $160m$ each. The area of the rectangle is less than that of the square by $100$ square meter. The length of the rectangle is

• A. $30m$
• B. $60m$
• C. $40m$
• D. $50m$

Answer 1

The correct option is D $50m$

Let length of rectangle be ${}^{\prime }{l}^{\prime }$ meters and breadth be ${}^{\prime }{b}^{\prime }$ meters.

Now, $2(l+b)=160m$

$\Rightarrow l+b=80m$ .....(1)

Let side of square be ${}^{\prime }{a}^{\prime }$ meters.

$\therefore$Perimeter of square$=4a=160m\Rightarrow a=40m$

Area of square-Area of rectangle$=100m^2$

${\left(40\right)}^2-lb=100m^2$

$\Rightarrow lb=1500$ ....(2)

From (1), $b=(80-l)$, put in (2), we get

$l(80-l)=1500$

$\Rightarrow 80l-l^2=1500$

$\Rightarrow l^2-80l+1500=0$

$\Rightarrow (l-50)(l-30)=0$

$\Rightarrow l=50,30$

$\therefore$ Length of rectangle$=50m$