RRB RPF RPSF SI and CONS Model Papers 10 with solutions

(4) Let the length and breadth of rectangle be x and y m. respectively.
According to the question,
2 (x + y) = 160
⇒ x + y = $\frac{160}{2}=80$ m ...(i)
Perimeter of square = 160 m
∴ Side of square $=\frac{160}{4}=40$ m
Now,
Area of rectangle = xy
Area of square= 40 × 40 = 1600 m${}^2$Then,
1600 – xy = 100
⇒ xy = 1600 – 100 = 1500 ..(ii)
Now,
(x – y)${}^2$ = (x + y)${}^2$ – 4xy
= (80)${}^2$ – 4 × 1500
= 6400 – 6000 = 400
⇒ x – y = $\sqrt{400}$ = 20 ...(iii)
From equations (i) and (iii),
2x = 100
⇒ x = $\frac{100}{2}=50$m.