Question

A rectangular plot of farmland will be bounded on one side by a river and on the other three sides by a​ single-strand electric fence. With 700 m of wire at your​ disposal, what is the largest area you can​ enclose, and what are its​ dimensions?

Answer 1

dimension are 350 m and 350 m and

area is 122500 m²

Explanation:

Given data

perimeter is 700 m

to find out

the largest area and its​ dimensions

solution

we consider x and y are the sides

so area is xy

perimeter is 2x+ y = 700

so we can say y = 700 -2x

so area will be = x (700 - 2x)

area = 700x - 2x²

we take derivative here and equal to zero

dA/dt = 700x - 2x²

700 - 4x = 0

x = 700/4

x = 175

so will be

y = 700 -2x

y = 700 -2(175)

y = 350

so dimension are 350 m and 350m

area is 122500 m²