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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 $x$?

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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 $x$?

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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 $x^{2}-15x=76$. Subtracting 76 from both sides of this equation yields $x^{2}-15x-76=0$. 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'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 $x$.

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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 $x$?

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