The length of a rectangle is two less than three times its width. If the area of the rectangle is 96 cm 2 , what is the length of the rectangle?

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Accepted Answer

If the width of the rectangle is x, then the length of the rectangle is 3x – 2. Since the area of a rectangle is equal to its length times its width, (x)(3x – 2) = 96, 3x 2 – 2x = 96, 3x 2 – 2x – 96 = 0, (3x + 16)(x – 6) = 0, and x = 6 (disregard the negative value of x since the width of a rectangle cannot be negative). Since x = 6, the length of the rectangle is equal to 3(6) – 2 = 18 – 2 = 16 cm.

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