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Harold Goldstein and his wife Elaine recently installed a built-in rectangular swimming pool measuring 23 feet by 47 feet. They want to add a decorative tile border of uniform width around all sides of the pool. How wide can they make the tile border if they purchased enough tile to cover 296 square feet?
Harold Goldstein and his wife Elaine recently installed a built-in rectangular swimming pool measuring 23 feet by 47 feet. They want to add a decorative tile border of uniform width around all sides of the pool. How wide can they make the tile border if they purchased enough tile to cover 296 square feet?
2 Answers
See below.
Explanation:
The pool is 23ft x 47 ft.
That makes the perimeter
Let the tile border width be
So you have :
Area of border =
So
Tiles come in standard sizes, You are unlikely to find a 2.1ft ( 25.37 inches) wide tile,
So they will have to decide tile size and how much is likleyto go waste.
The tile border can be 2 feet wide
Explanation:
I modeled this as two rectangles. The inner one is the pool, and the outer one is the area of the border. If you take the difference in the areas of the rectangle you get the area coverage of the border:
Where
The outer length and width is equal to the inner length width increased by twice the border thickness, since its the same thickness on each side.
Where
Now, we substitute our solutions for
Now, we have a quadratic and we can solve for
Now, we have two solutions for