Question

Cynthia Besch wants to buy a rug for a room that is 18 ft wide and 35 ft long. She wants to leave a uniform strip of floor around the rug. She can afford to buy 200 square feet of carpeting. What dimensions should the rug​ have?

Answer 1

Explanation:

Let the width of the rug be x ft. Then the length of the rug will be (18-2x) ft (since she wants to leave a uniform strip of floor around the rug).

The area of the rug can be expressed as:

x(18-2x) = 18x - 2x^2

We know that the area of the rug should be 200 sq ft, so we can set up the equation:

18x - 2x^2 = 200

Simplifying this equation, we get:

x^2 - 9x + 100 = 0

Using the quadratic formula, we can solve for x:

x = [9 ± sqrt(9^2 - 4(1)(100))] / 2

x = [9 ± sqrt(281)] / 2

Since the width of the rug cannot be negative, we can take the positive value of x:

x = [9 + sqrt(281)] / 2

x ≈ 9.88 ft

Therefore, the width of the rug should be about 9.88 ft, and the length of the rug should be about (18-2(9.88)) = 0.24 ft. However, this is not a realistic length, so we should adjust the size of the uniform strip of floor that Cynthia wants to leave around the rug.