A knitter wants to make a rug for a dollhouse. The length of the rug will be 2 inches more than it’s width. The total area of the rug ( in square inches) based on the width W of the rug (in inches ) is given by A(w) = w (2+w) If the desired area of the rug is 15 square inches, what is the width of the rug, in inches?

The length of the rug will be 2 inches more than it’s width
The total area of the rug ( in square inches) based on the width w of the rug (in inches ) is given by A(w) = w (2 + w)
The desired area of the rug is 15 square inches

We need to find the width of the rug

∵ The area of the rug is A(w) = w(2 + w)

- Simplify the right hand side

∴ A(w) = 2w + w²

∵ The desired area of the rug is 15 square inches

- Equate A(w) by 15

∴ 2w + w² = 15

- Subtract 15 from both sides

∴ 2w + w² - 15 = 0

- Its a quadratic equation arrange its terms from the greatest power of x

∴ w² + 2w - 15 = 0

Factorize it into two binomial factors

∵ w² = w × w

∵ 15 = 3 × 5

∵ 5w - 3w = 2w

∴ w² + 2w - 15 = (w -3)(w + 5)

∴ (w - 3)(w + 5) = 0

- Equate each factor by 0

∴ w - 3 = 0 OR w + 5 = 0

∵ w - 3 = 0

- Add 3 to both sides

∴ w = 3

∵ w + 5 = 0

- Subtract 5 from both sides

∴ w = -5 ⇒ rejected because no dimension with -ve value

∴ w = 3 only

The width of the rug is 3 inches

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You can learn more about the quadratic equation in brainly.com/question/9328925

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