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Advanced Math / Nonlinear functions Difficulty: Medium

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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Explanation

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 equals l w , where A is the area, l 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 l equals 2 w. 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 equals, 2 w times w . This equation can be rewritten as 162 equals, 2 w squared. Dividing both sides of this equation by 2 yields 81 equals, w squared. Taking the square root of both sides of this equation yields plus or minus 9 equals 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 equals, 2 w plus w instead of 162 equals, 2 w times w.