Question

A farmer wants to fence in a rectangular field of livestock. The boundary for one side of the field is a long, straight river. No fencing is needed on this side. For the remaining three sides, he has 400 meters of fencing available. What are the dimensions of the largest rectangular area that can be formed

Answer 1

Answer:

To get maximum area, the dimensions will be;

l = 200 and b = 100

Step-by-step explanation:

Given the data in the question;

No fencing is needed on this side as the farmer wants to fence 3 sides of a rectangular field with 400 m fencing.

now, let the two vertical length sides be x meter and the horizontal length be 400 - 2x

as shown in the image below;

so,

Area of rectangle = (400 - 2x) × x = 400x - 2x²

now, to maximize area 'A', we will make A' = 0

⇒ 400 - 2(2x) = 0

400 = 4x

x = 400/4 = 100

so

⇒ (400 - 2x) = 400 - 2(100) = 400 - 200 = 200

∴ Maximum area = ( 400 - 2x) × x

= 200 × 100

= 20000 m²

∴ To get maximum area, the dimensions will be;

l = 200 and b = 100