Half the perimeter of rectangle garden, whose length is 4m more than its width, is 36 cm. Find the dimensions of the garden.

Solution :

Let x be the length of garden and y be its width.

Then,

According to question, perimeter = 2(length +width) = 2(x + y)

Therefore, half perimeter = (x + y)

But it is given as 36

\(\therefore\) (x + y) = 36

Also, x = y + 4

Now, we form the table given below for both the equations to find the solutions graphically.

For equation, x + y = 36

If x = 20, y =16

If x = 24, y = 12

x	20	24
y	16	12

For equation, x – y = 4

If x = 10, y = 6

If x = 16, y = 12

x	10	16
y	6	12

Now plot the points in the table on the graph.

We see that lines intersect at point (20,16) as shown in the graph.

Hence, Length = 20 m and width = 16 m