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 \\(14.8\text{ yd}\\).

part: 1 / 2
part 2 of 2
the width is approximately \\(\text{yd}\\).

Explanation:

Set up the geometric equation

Using the Geometric Word Problems knowledge point
Let \(L\) be the length of the carpet in yards.
The width \(W\) is \(2\text{ yd}\) less than the length:

$$W = L - 2$$

The area of the rectangular carpet is \(190\text{ yd}^2\):

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

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

Solve the quadratic equation

Using the Quadratic Formula knowledge point

$$
LATEXBLOCK0
$$

Calculate numerical values

Since length must be positive:

$$
LATEXBLOCK1
$$

Answer:

Question 1

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

Question 2

The width is approximately <blank>12.8</blank> yd.