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

The perimeter of the square = 160 m.
Side of square = (160/4) m
= 40 m.
Area of square = (40 × 40) m² = 1600 m²
Area of rectangle = (1600 - 100) m² = 1500 m²
Let the length and breadth of the rectangle be 'l' and 'b' respectively.
Then, 2(l + b) = 160
⇒ (l + b) = 80
⇒ b = 80 - l.

∴ lb = 1500
⇒ l(80 - l) = 1500
⇒ 80l - l² = 1500
⇒ l² - 80 l + 1500 = 0
⇒ (l - 50)(l - 30) = 0
⇒ l = 50. or l = 30

Hence, length = 50 m, breadth = 30 m.