Question

Justin wants to use 376 ft of fencing to fence off the greatest possible rectangular area for a garden. What dimensions should he use? What will be the area of the garden?
A. 89 x 99; 8811 ft
B. 92 x 96; 8832 ft
C. 94 x 94; 8836 ft
D. 93 x 95; 8835 ft

please don't just provide the answer I would like to know how, will fan and medal

Answer 1

http://www.cymath.com/

Answer 2

The perimeter of the rectangle is P = 2*(L+W). Plug in P = 376 and isolate L

P = 2*(L+W)
376 = 2*(L+W)
376/2 = 2*(L+W)/2
188 = L+W
L+W = 188
L = 188-W

now plug this into A = L*W

A = L*W
A = (188-W)*W
A = 188W - W^2
A = -W^2 + 188W

If you replace A with y, and replace W with x, you will get this equation

y = -x^2 + 188x

finding the vertex of that equation leads you to the max area (and the dimensions needed to get the max area)