A rectangle has a length of 15 feet less than 6 times its width. If the area of the rectangle is 561 square feet, find the length of the rectangle.

**w = width**

6w - 15 = length{length is 15 less than 6 times the width}

6w - 15 = length

**Area of a rectangle = width x length**

w(6w - 15) = 561 {substituted width and length into area formula}

6w² - 15w = 561 {used distributive property}

6w² - 15w - 561 = 0 {subtracted 561 from each side}

w = 11 or -8.5 {used the quadratic formula}

Only using the positive measurement for width.

6w - 15 = 51 {substituted 11, in for width, into (6w - 15) to find the length}

width = 11 ft

**length = 51 ft**

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