Question

The length of a rectangle is three times longer than its width. The perimeter of the rectangle is 16 feet. If x represents the width of the rectangle, which equation can be used to find its value?

Answer 1

To find the width of the rectangle, where the length is three times the width and the perimeter is 16 feet, use the equation 16 = 2(3x) + 2x. Solving for x yields the width of the rectangle.

Step-by-step explanation:

The student is asked to find an equation that represents the width of a rectangle, given that the length of the rectangle is three times longer than its width and the perimeter is 16 feet. If we let x represent the width, then the length can be expressed as 3x. To find the perimeter of a rectangle, we use the formula P = 2l + 2w, where P is the perimeter, l is the length, and w is the width.

Now, let’s set up an equation using the given perimeter (16 feet):
16 = 2(3x) + 2x.

Steps to solve:

Substitute the known values into the perimeter formula: 16 = 2(3x) + 2x.

Simplify the equation: 16 = 6x + 2x.

Combine like terms: 16 = 8x.

Finally, divide both sides by 8 to solve for x: x = 2.

By substituting this value back into the length and width expressions, we can validate that our equation and solution are correct.

Answer 2

Given that x represents the width of the rectangle and that the length of the rectangle is three times longer than the width. Then the length is 3x. The perimeter of a rectangle is given by 2(length + width) = 2(3x + x) = 2(4x) = 8x. The perimeter of the rectangle is 16 feet. Therefore, the required equation is 8x = 16.