Find the dimensions of the pen

​A person's rectangular dog pen for his dog must have an area of 200 square feet. Also, the length must be 20 feet longer than the width. Find the dimensions of the pen.

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w = width
w + 20 = length {the length is 20 feet longer than the width}

Area of a rectangle = width x length

w(w + 20) = 200 {area of a rectangle is width x length}
w² + 20w = 200 {used distributive property}
w² + 20w - 200 = 0 {subtracted 200 from each side}

This quadratic equation cannot be factored, so the quadratic formula may be used.

a = 1, b = 20, and c = -200

This gives two possible solutions:

Since the width of a rectangle cannot be negative, w ≈ 7.32.

To find the length, substitute 7.32, in for w, into w + 20.
w + 20 {the length}
≈ 7.32 + 20 {substituted the width, 7.32, into the length, w + 20}
≈ 27.32 {added}

width ≈ 7.32 feet
length ≈ 27.32 feet

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