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You are constructing a triangular sail for a one-person sailboat. For support, a horizontal steel pole will run along the base of the sail and a vertical steel pole will run from the base to the top of the sail. In order for the sailboat to function properly, the combined weight of the poles cannot exceed 80 pounds. If the steel poles weigh 5 pounds per foot, what is the area of the largest sail you can build? Fully justify your answer; in particular, you must show that the area you found is indeed the largest possible.

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Answer:

8 by 8.

Step-by-step explanation:

A triangular sail to be constructed with a vertical and a horizontal poles for support. The combined weight of the poles cannot exceed 80 pounds and the poles weigh 5 pounds per foot gives us a total length of 80/5=16 feet. Let us call the length of horizontal pole by x and we have (16-x) for the vertical one. We want to maximize area of the sail, so  [tex] A(x)= x (16-x)/2 [\tex] is the function we want to maximıze on [0, 16].

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