SOLUTION: John is building a pen in his backyard. the sides of the pen will form a right triangle with his home. the legs (base and height) of the triangle will be the pen material and the r
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Question 1157421: John is building a pen in his backyard. the sides of the pen will form a right triangle with his home. the legs (base and height) of the triangle will be the pen material and the remaining side (hypotenuse) will be formed by his home. in other words, he only needs fencing for the legs of the triangular region. you may assume the side of his home is as long as necessary. given that he only has 50 feet of material for the wall what is largest possible area of his backyard? Answer by ikleyn(52890) (Show Source):
Let x and y be the sides (the legs) of this right angled triangle.
You have the total length of the legs given x + y = 50 feet,
and you want maximize the area A = .
Express y = 50-x.
Then for the area, you have this formula
A(x) = = - + 25x.
This quadratic function gets the maximum at x = - = = 25 feet.
So, the optimum length for both legs is x = 25 feet = y,
and the maximum area is = = 312.5 square feet.
