Abc daycare wants to build a fence to enclose a rectangular playground. the area of the playground is 980 square feet. the fence along three of the sides costs $5 per foot and the fence along the fourth side, which will be made of brick, costs $10 per foot. find the length of the brick fence that will minimize the cost of enclosing the playground. (round your answer to one decimal place.)

Let the length of the brick fence be x and the length of the adjacent side of the brick fence y. Then
Area of the rectangular playground is given by xy = 980 square feet.
The cost of enclosing the playgroung is given by C = 10x + 5x + 5(2y) = 15x + 10y
From xy = 980, y = 980/x
Thus, C = 15x + 10(980/x) = 15x + 9800/x
For minimum cost, dC/dx = 0
dC/dx = 15 - 9800/x^2 = 0
9800/x^2 = 15
15x^2 = 9800
x^2 = 9800 / 15 = 653.33
x = sqrt(653.33) = 25.56 = 25.6

Therefore, the length of the brick fence that will minimize the cost of enclosing the playground is 25.6 feet.

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