17. The perimeter of a rectangle is 44 cm. If its length is increased by 4 cm and its breadth is increased by 2cm, its area is increased

by 72 sqcm. Find the dimensions of the rectangle.

Let the length of the rectangle = l cm breadth = b cm

Then perimeter = 44

= 2(l + b) = 44 = l + b = 44/2

= l + b = 22 .........(1)

Area of rectangle = lb

New length after increase = (l + 4) cm

New breadth after increase = (b + 2) cm

New area of rectangle after increase = (l + 4)(b + 2)

New area of rectangle after increase = lb + 2l + 4b + 8

Acc. to question

lb + 2l + 4b + 8 - lb = 72

 2l + 4b = 64

 l + 2b = 32 ........(2) ( Dividing both sides by 2)

Subtracting equation (1) from equation (2)

l + 2b - l - b = 32 - 22

= b = 10

Putting value of b in equation (1) we get

l + 10 = 22

= l = 22 - 10 = l = 12

Thus l = 12 cm and b = 10 cm