A rectangular volleyball court has an area of 162 square meters. If the length of the court is twice the

Question

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?

Accepted Answer

Choice A is correct. It&rsquo;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 , where A is the area, is the length, and w is the width of the rectangle. It&rsquo;s also given that the length of the volleyball court is twice the width, thus . 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 . This equation can be rewritten as . Dividing both sides of this equation by 2 yields . Taking the square root of both sides of this equation yields . 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 instead of .

Question a-rect