09.07.2022 - 19:14

# Tennis court dimensions: A regulation tennis court for a singles match is laid out so that it’s length is 3 ft less than three times its width. The area of the singles court is 2106 ft^2.

Question:

Tennis court dimensions: A regulation tennis court for a singles match is laid out so that it’s length is 3 ft less than three times its width. The area of the singles court is 2106 ft{eq}^2. {/eq} What is the length and width of the singles court?

Answers (1)
• April 2, 2023 в 16:35
Let's assume that the width of the tennis court is x feet. According to the problem, the length of the court is 3 feet less than three times its width. So we can express the length as (3x - 3) feet. The area of the court is given as 2106 ft{eq}^2{/eq}. We know that the area of a rectangle is equal to its length multiplied by its width. Therefore, we can set up the equation: (3x - 3) * x = 2106 Expanding the left side of the equation, we get: 3x^2 - 3x = 2106 Subtracting 2106 from both sides, we get: 3x^2 - 3x - 2106 = 0 We can solve this \quadratic equation by using the \quadratic formula: x = (-b ± sqrt(b^2 - 4ac)) / 2a where a = 3, b = -3, and c = -2106. Plugging in these values, we get: x = [-( -3) ± sqrt((-3)^2 - 4(3)(-2106))] / 2(3) x = [3 ± sqrt(9 + 25272)] / 6 x = [3 ± sqrt(25281)] / 6 x ? 37.9 or x ? -19.9 Since the width of the court cannot be negative, we can discard the negative solution. Therefore, the width of the court is \approx imately 37.9 feet. Using the expression we derived earlier for the length of the court in terms of its width, we can find the length: Length = 3x - 3 Length = 3(37.9) - 3 Length ? 107.7 Therefore, the length and width of the singles tennis court are \approx imately 107.7 feet and 37.9 feet, respectively.
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