Question

2. Two rectangular fields with identical shapes and areas are to be fenced side by side. The total area enclosed is 8mi^2 and the perimeter for all the fencing is 16 miles. Find the possible dimensions of one of the fields (2 possible answers).

Answer 1

Explanation:

Let length is x and breadth is y.

The formula for the area and the perimeter of a rectangle is given by :

A = xy

P = 2(x+y)

Here, A = 8 mi² and P = 16 miles

Putting all the values,

xy = 8

y=8/x ......(1)

2(x+y) = 16

x+y = 8 .....(2)

Put equation (2) in equation (1) as follows :

`x+(8)/(x)=8\\\\x^2+8=8x\\\\x^2-8x+8=0`

When we solve, we get :

x = 6.82 miles, 1.17 miles

Put the value of x in equation (1)

When x = 6.82 miles,

y = 8/6.82

y = 1.17 miles

When x = 1.17 miles,

y = 8/1.17

y = 6.82 miles

Hence, the dimension of the field is 6.82 miles and 1.17 miles.