Question

A rectangle is 8 cm long and b cm broad.find the range of value of b if the perimeter of the rectangle is not geater than 50 cm and not less than 18 cm.

Answer 1

length ( l ) = 8cm

breadth ( b ) = b cm

perimeter = 2 × ( l + b )

Case 1

perimeter > 18, let perimeter ( p ) = 18

p = 2 × ( l + b )

18 = 2 × ( 8 + b )

18 = 16 + 2b

2b = 18 - 16

2b = 2

b = 1 or b > 1

Case 2

perimeter < 50, let perimeter ( p ) = 50

p = 2 × ( l + b )

50 = 2 × ( 8 + b )

50 = 16 + 2b

2b = 50 - 16

2b = 34

b = 34/2

b = 17 or b < 17

so, breadth should be greater than 1 cm and less than 17 cm.