Q. Half the perimeter of a rectangular garden, whose length is 4 m � more than its width, is 36m. Find the dimensions of the garden.
Sol :
Let the length of rectangle be x m & breadth of rectangle be y m.
According to the first condition,
1
2
×
[2
(x
+
y)
]
=
36
∴
x
+
y
=
36
According to the second condition,
x
=
y
+
4
.... (ii)
Now to represent graphically, we find two solutions of each equation
x
+
y
=
36
x
=
y
+
4
x
y
(x, y)
0
36
(0, 36)
36
0
(36, 0)
x
y
(x, y)
8
4
(8, 4)
4
0
(4, 0)
Scale
1 cm = 4m on both the axes
Y
X′
Y′
0
X
4
12
8
20
16
28
24
32
36
40
4
8
12
16
20
24
28
32
36
40
(0 , 36)
(36 , 0)
X + y = 36
(8,4)
(4,0)
(20 , 16)
X + y = 4
The length of rectangle is 20m and breadth of rectangle is 16m.
Perimeter = 2(l + b)
.... (i)