Answer:
Area = 200x - x², Max area is 10000m² with dimensions 100m × 100m
Step-by-step explanation:
Total fencing = perimeter
Let length of the sides be x and y,
2(x + y) = 400
x + y = 200
y = 200 - x
Area = x × y
= x(200 - x)
Area = 200x - x²
For max area, convert area into the completed square form
-(x² - 200x)
-(x² -2(x)(100) + 100² - 100²)
-[(x - 100)² - 10000]
-(x - 100)² + 10000
Max area is 10000 m²
Because the least value of (x - 100)² is 0.
That too when x = 100
When x = 100,
y = 200 - x = 200 - 100 = 100
Dimensions are 100m × 100m
