Part A: Determine X so the area of the deck is Maximal and determine the angle a

Question

Part A: Determine X so the area of the deck is Maximal and determine the angle at the right end of the deck.

Part B: Suppose the fencing is bendable What is the shape and area of the maximal deck?

A picture is below to better explain the problem:

a. You have 4 straight, 10 pieces of fence which you will use to enclose a deck alongside the back of your house. Find the dimensions of the deck with the largest area. See the picture below. Use Calculus. Justify that your answer is the maximum. - Specifically, determine x such that the area is maximal. Also determine the angle at the right end of the deck. b Suppose the fencing is bendable. What is the shape and area of the maximal deck (You may not be able o prove your answer is correct.)

Explanation / Answer

its a very small deck. For the 4 sided deck use a square 10 inches on each side. Wow! That is less than 1 square foot for the whole deck. Oh, wait, you don't need fence on the house side, so how about 20 inches on the far-from-the house side and 10 inches on each of the going out from the house side. Now its 200 square inches, which is larger than 1 square foot, because 1 square foot is 144 square inches. If the pieces can be bent, a circle would give the largest area. Maybe you can do better, but its such a small deck it is hardly worth the trouble.

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