(Q.23). The perimeter of a rectangular plot is 32m. If the length is increased by 2m and the breadth is decreased by 1m, the area of the plot remains the same. Find the length and breadth of the plot.

Let length and breadth of the rectangular land be l and b respectively. Then,

area = lb and

Perimeter = (l + b) = 32 m

Then, l + b = which implies l + b - = 0 ... (1)

When length is increased by 2 m., then new length is l + . Also breadth is decreased by 1m; so new breadth is b -

Then, area = (l + ) (b - )

Since there is no change in the area.

(l + 2) (b - 1) = lb

- l +2b - = lb or lb - lb = l - 2b + 2

l - b + = ... (2)

For the equation l + b - 16 = 0
l b = 16 - l (l,b)
6 b = 16 - = (6,)
8 b = 16 - = (8,)
10 b = 16 - = (10,)
12 b = 16 - = (12,)
14 b = 16 - = (14,)
For the equation l - 2b + 2 = 0
l
b =
l + 2
2
(l,b)
6
b =
+ 2
2
 =
(6,)
8
b =
+ 2
2
 =
(8,)
10
b =
+ 2
2
 =
(10,)
12
b =
+ 2
2
 =
(12,)
14
b =
+ 2
2
 =
(14,)

So, original length of the plot is m and its breadth is m

Taking measures of length on X-axis and measure of breadth on Y-axis, we get the graph.