Given a rectangle with a fixed perimeter of 24 meters if we increase the length by 1m the width and area will vary accordingly. Use the following table of values to look at how the width and area vary as the length varies.

What do you observe? Write your observations in your note books

Given: Perimeter of the rectangle P = 2(l+b) = 24m

To find: Variation of width and area with length if perimeter is fixed.

Area = lxb

Add length and breadth and multiplying by 2 should give 24.

(Note: All lengths are in cm, all areas are in cm²)

l = 3, P = 24 2(l+b) = 24 = 2(3+b) b = 9, A = 27

l = 4, P = 24 2(l+b) = 24 = 2(4+b) b = 8, A = 32

l = 5, P = 24 2(l+b) = 24 = 2(5+b) b = 7, A = 35

l = 6, P = 24 2(l+b) = 24 = 2(6+b) b = 6, A = 36

l = 7, P = 24 2(l+b) = 24 = 2(7+b) b = 5, A = 35

l = 8, P = 24 2(l+b) = 24 = 2(8+b) b = 4, A = 32

l = 9, P = 24 2(l+b) = 24 = 2(9+b) b = 3, A = 27

Observation: Length and breadth are inversely proportional to each other if perimeter is kept constant. Area first increases with length then decreases.