If the perimeter of a certain rectangle is 50 units and its area is 114 sq. units, then how many units is breadth shorter than length ?

15 10 12 13

13

Perimeter of rectangle = 2 (l+b)                      ⇒ 50 = 2(l+b)                       ⇒ (l+b) = 25  Area of rectangle = l × b Now, (l - b)2 = (l + b)2 - 4lb ⇒ (l - b)2 = 252 - (4 × 114) = 625 - 456 = 169 ⇒ l - b = \(\sqrt {169}\) = 13