Question

The perimeter of a rectangle and a square are both 160m but the area of the former is is less than the area of the latter by 100sqm find the length and the breadth of the rectangle

Answer 1

The perimeter of rectangle = 160m =2(l+b)

                                                l+b = 80   .........(1)

The perimeter of square = 160m = 4s

Therefore the side of square s = 160/4

                                            s = 40m

Area of rectangle is less than square by 100sqm

Area of rectangle = Area of square - 100

l*b = s*s - 100

l*b = 40*40 -100

l*b = 1600 -100 = 1500                   .........(2)

Now substitute the value of b from equation(1) to equation(2)

b =80-l

l*(80-l) = 1500

80l - l2 = 1500

l2 - 80l +1500=0

l= 30,50

Therefore, there are two possible values of length and breadth

(1) l = 30m & b=50m

(2) l = 50m & b= 30m