SSC Selection Post 2022 PYQ — Question 52

The correct answer is option 4 i.e. 50 m.

Perimeter of rectangle = 160 → l + b = 80

Area of rectangle = 1500 m² (since square's area is 1600 and rectangle is 100 less)

$lb = 1500 \quad$ and $\quad l + b = 80$

b = 80 - l  into the area:

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

⇒ $l = \frac{80 \pm \sqrt{80^2 - 4 \cdot 1500}}{2} = \frac{80 \pm \sqrt{6400 - 6000}}{2} = \frac{80 \pm \sqrt{400}}{2} = \frac{80 \pm 20}{2}$

l = 50 or l = 30

The greater as length = 50 meters