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A rectangular volleyball court has an area of 162 square meters. If the length of the court is twice the width, what is the width of the court, in meters?

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A rectangular volleyball court has an area of 162 square meters. If the length of the court is twice the width, what is the width of the court, in meters?

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Choice A is correct. It's given that the volleyball court is rectangular and has an area of 162 square meters. The formula for the area of a rectangle is $A=\\ell\\cdot W$, where A is the area, $\\ell$ is the length, and $W$ is the width of the rectangle. It's also given that the length of the volleyball court is twice the width, thus $\\ell=2W$. Substituting the given value into the formula for the area of a rectangle and using the relationship between length and width for this rectangle yields $162=(2W)(W)$. This equation can be rewritten as $162=2W^{2}$. Dividing both sides of this equation by 2 yields $81=W^{2}$. Taking the square root of both sides of this equation yields $\\pm 9=W$. Since the width of a rectangle is a positive number, the width of the volleyball court is 9 meters.

Choice B is incorrect because this is the length of the rectangle. Choice C is incorrect because this is the result of using 162 as the perimeter rather than the area. Choice D is incorrect because this is the result of calculating $W$ in the equation $162=2W+W$ instead of $162=(2W)(W)$.

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A rectangular volleyball court has an area of 162 square meters. If the length of the court is twice the width, what is the width of the court, in meters?

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