A rectangular deck is to be constructed using a rock wall as one side and fencing for the other three sides. There are 24 yards of fencing available. Determine the dimensions that would create the deck of maximum area. What is the maximum area? Enter only the maximum area. Do not include units in your answer.

Question

Mathematics

Pebbles

24 October, 01:17

A rectangular deck is to be constructed using a rock wall as one side and fencing for the other three sides. There are 24 yards of fencing available. Determine the dimensions that would create the deck of maximum area. What is the maximum area? Enter only the maximum area. Do not include units in your answer.

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Answers (1)

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Ewing · Answer 1

Area is maximum when x=6

Step-by-step explanation:

2x + y = 24

y=24 - 2x

area of fencing is given as

A=xy

=x (24-2x)

= 24x-2x²

A = 24x-2x²

d/dx (A) = d/dx (24x-2x²)

= 24 - 4x

Equating it to 0

0 = 24 - 4x

x = 6

taking second derivative is

d/dx (dA/dx) = d/dx (24-4x)

= - 4

Hence area is maximum x = 6