Question

a rectangular piece of carpet covers \\(190\text{ yd}^2\\). the width is \\(2\text{ yd}\\) less than the length. find the length and width. round your answers to the nearest tenth of a yard.

part: 0 / 2

part 1 of 2

the length is approximately yd.

Explanation:

Set up the quadratic equation

Let \(L\) represent the length of the rectangular carpet in yards.
The width \(W\) is \(2\text{ yd}\) less than the length:

$$W = L - 2$$

The area of the rectangle is given as \(190\text{ yd}^2\):

$$L(L - 2) = 190$$

$$L^2 - 2L - 190 = 0$$

Solve using the quadratic formula

Using the Quadratic Formula knowledge point

$$
LATEXBLOCK0
$$

Calculate the approximate length

Since length must be positive:

$$L = 1 + \sqrt{191}$$

$$\sqrt{191} \approx 13.820$$

$$L \approx 1 + 13.820 = 14.820$$

Rounding to the nearest tenth:

$$L \approx 14.8\text{ yd}$$

Answer:

The length is approximately <blank>14.8</blank> yd.