A man wishes to have a rectangular shaped garden in his backyard. He has 84 feet of fencing with which to enclose his garden. a) Write an expression for the perimeter of the garden. b) The area of the garden is A = l*w. Use the perimeter equation from part (a) to write the area in terms of just one variable. c) Find the dimensions for the largest area garden he can have if he uses all the fencing.

Question

Mathematics

Rowan Brady

2 October, 21:02

A man wishes to have a rectangular shaped garden in his backyard. He has 84 feet of fencing with which to enclose his garden. a) Write an expression for the perimeter of the garden. b) The area of the garden is A = l*w. Use the perimeter equation from part (a) to write the area in terms of just one variable. c) Find the dimensions for the largest area garden he can have if he uses all the fencing.

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Answers (1)

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Keaton Owen · Answer 1

84=2l+2w

w=21

Step-by-step explanation:

84=2 (l+w)

42=l+w

l=42-w

Area=l*w

A = (42-w) * w

Differentiate A=42w-w*w

with respective to "w".

dA/dw = 42-2w

For a minimum or maximum area

dA/dw=0

then, 42-2w=0

w=21

proving "A" is maximum when "w=21"

dA/dw>0 when w<21

dA/dw21

Therefore Area is maximum when "w=21"