A rectangle has a length of x units and a width of x - 15 units. If the rectangle has

Question

A rectangle has a length of x units and a width of x - 15 units. If the rectangle has an area of 76 square units, what is the value of x ?

Accepted Answer

Choice B is correct. The area of a rectangle is equal to its length multiplied by its width. Multiplying the given length, x units, by the given width, x - 15 units, yields x x - 15 square units. If the rectangle has an area of 76 square units, it follows that x x - 15 = 76 , or x 2 - 15 x = 76 . Subtracting 76 from both sides of this equation yields x 2 - 15 x - 76 = 0 . Factoring the left-hand side of this equation yields x - 19 x + 4 = 0 . Applying the zero product property to this equation yields two solutions: x = 19 and x = - 4 . Since x is the rectangle&rsquo;s length, in units, which must be positive, the value of x is 19 . Choice A is incorrect. This is the width, in units, of the rectangle, not the value of x . Choice C is incorrect and may result from conceptual or calculation errors. Choice D is incorrect. This is the area, in square units, of the rectangle, not the value of x .

Question a-rect