Question

The owner of the Rancho Los Feliz has 7000 yd of fencing with which to enclose a rectangular piece of grazing land along the straight portion of a river. Fencing is not required along the river, and the length of the fencing parallel to the river is to exceed the length of the fencing perpendicular to it by 2500 yd. Find the area of the enclosed land (in sq yd).

Answer 1

Area of land = 6000000 sq yd

Explanation:

Given,

length of fencing= 7000 yd

Let's assume that the length of the land parallel to the river is l and the breadth of the land perpendicular to the river is b.

Then, it is given that

l = b +2500

Since, there is no need of fencing along the river so, we can write

l +2b = 7000

=>b+2500 = 7000

=> b = 7000-2500

= 4000

As the area of rectangular land can be given as

A = length x breadth

= 4000 x 2500 sq yd

= 6000000 sq yd

So, the area of the enclosed land will be 6000000 sq yd.

Answer 2

6000000 sq yd

Explanation:

Data provided in the question:

Length of the fencing = 7000 yd

let the perpendicular sides be 'P'

and the length parallel to the river be 'L'

according to the given question

L = P + 2500 ............(1)

also,

Length to be fenced = 2P + L

thus,

2P + L = 7000 ...........(2)

substituting L from (1), we get

2P + P + 2500 = 7000

or

3P = 7000 - 2500

or

3P = 4500

or

P = 1500 yd

Thus,

L = 1500 + 2500 = 4000 yd

Therefore,

the area of the rectangular land = L × P = 4000 × 1500 = 6000000 sq yd