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.
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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.
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