Question

Thrice the perimeter of a rectangular garden, whose length is 4 m more than its width, is 54 m. Find the dimensions of the garden by the graphical method.

Answer 1

Let the garden's width be x and its length be y.

Then, according to the question,

y = 4 + x

And 3[2(y + x) = 54  ...(i)

⇒ 6 (y + x) = 54

⇒ y + x = 9  ...(ii)

For equation (i):

x	0	– 4
y = 4 + x	4	0
(x, y)	(0, 4)	(– 4, 0)

For equation (ii):

x	0	9
y = 9 – x	9	0
(x, y)	(0, 9)	(9, 0)

Thus, the graphical representation is as follows:

The two lines cross at point (2.5, 6.5)

As a result, the garden's length is 6.5 m and its breadth is 2.5 m.