Question

A rectangle has a perimeter of 200 meters, with the length four times its width. What is its width?

Answer 1

The rectangle's width is 20 meters, determined by solving the perimeter equation with the given length-to-width ratio.

Step-by-step explanation:

To determine the width of the rectangle, we utilize the formula for the perimeter of a rectangle: (2L + 2W = P), where (L) is the length, (W) is the width, and (P) is the perimeter. The problem specifies that the length is four times the width (L = 4W).

Substituting this relationship into the perimeter formula and given that the perimeter is 200 meters, we can set up the equation (2(4W) + 2W = 200) to represent the situation.

Solving for (W), we get (W = 20). Therefore, the width of the rectangle is 20 meters. This conclusion is reached by understanding the geometric properties of rectangles and employing algebraic methods to solve for the unknown width.

Answer 2

The width of the rectangle is 20 meters.

Step-by-step explanation:

A rectangle's perimeter is given by the formula (P = 2l + 2w), where (l) is the length and (w) is the width. In this case, we are given that the rectangle's perimeter is 200 meters, and the length is four times its width. Let's denote the width as (w) and the length as (l).

The formula for the perimeter can be expressed as
`\(P = 2(4w) + 2w\),`since the length is four times the width. Simplifying this equation gives (P = 10w). Given that the perimeter is 200 meters, we can set up the equation (10w = 200) and solve for (w).

`\[ w = (200)/(10) = 20 \]`

Therefore, the width of the rectangle is 20 meters.

In summary, the width of the rectangle is found by setting up and solving the equation derived from the perimeter formula. By substituting the given values and performing the calculations, we determine that the width is 20 meters. This approach ensures clarity in understanding the problem and arriving at the correct solution.