Question

Please Help!!!!

Kellie wants to cover part of the lawn with pavers to make a nice place to put a table and some chairs. This space will be a rectangle with an area of 108 square feet, and the rectangle will be 3 feet longer than wide. What will the dimensions of this rectangle be? In other words, what will the length and width be?

For the record, the formula for the area of a rectangle is A = LW.

8a) Clearly write out the equation you would use to answer the question.

8b) Answer the question. What will the dimensions be? Please write your answer as a complete sentence with appropriate units.

Answer 1

8a)

x = width

x+3 = length, since its 3 ft longer than the width

A = length*width

A = LW

A = (x+3)*x

A = x^2+3x

Set this equal to 108 since this is the area of the rectangle.

Answer: x^2 + 3x = 108

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8b)

x^2+3x = 108

x^2+3x-108 = 0

Use the quadratic formula with a = 1, b = 3, c = -108

`x = (-b\pm√(b^2-4ac))/(2a)\\\\x = (-(3)\pm√((3)^2-4(1)(-108)))/(2(1))\\\\x = (-3\pm√(441))/(2)\\\\x = (-3\pm21)/(2)\\\\x = (-3+21)/(2) \ \text{ or } \ x = (-3-21)/(2)\\\\x = (18)/(2) \ \text{ or } \ x = (-24)/(2)\\\\x = 9 \ \text{ or } \ x = -12\\\\`

Ignore the negative solution because we cannot have a negative width.

x = 9 is the width

x+3 = 9+3 = 12 is the length being 3 longer.

The rectangle is 12 ft by 9 ft to get an area of 12*9 = 108 sq ft, which confirms the answer.

Answer: 12 feet by 9 feet