Question

An ecology center wants to set up an experimental garden using 400 meters of fencing to enclose a rectangular area of 9900 square meters. Find the dimensions of the garden. ​ (Note that the fencing will be the perimeter of the​ garden, and the formula for the perimeter of a rectangle is P​ = 2L​ + 2W.)

Answer 1

Explanation:

Given that,

Fencing to be done, P = 400 m

Area of the rectangular garden, $A=9900\ m^2$

Let l is the length and b is the breadth of the garden. The area of the rectangle is given by :

$A=l\times b$

$lb=9900$............(1)

The perimeter of the garden is given by :

$P=2(l+b)$

$400=2(l+b)$

$200=(l+b)$...............(2)

On solving equation (1) and (2), we get the value of l and b are as follows :

l = 90 m and b = 110 m

or

b = 90 m and l = 110 m

So, the dimension of the garden is 90 m by 110 m. Hence, this is the required solution.