Question

you have 1000 feet of fencing to enclose a rectangular playground and subdivide it into two smaller playgrounds by placing the fencing parallel to one of the sides. What is the largest possible area of the playground

Answer 1

Largest AREA A = x × y = 250 × 500/3 = 125000 / 3 = 41666.67 ft²

Dimensions; X = 250 ft and Y = 500/3 ft

Explanation:

Given the data in the question;

2x + 3y = 1000 -------- EQU 1

2x = 1000 - 3y

x = 500 - 3y/2

AREA = x × y = (500 - 3y/2)y

= 500y - 3/2y²

dA/dxy = 500 - 3y = 0

3y = 500

y = 500/3

so from equ 1

2x + 3(500/3) = 1000

2x = 1000 - 500

x = 250

So; Largest AREA A = x × y = 250 × 500/3 = 125000 / 3 = 41666.67 ft²

Dimensions; X = 250 ft and Y = 500/3 ft