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
