Question

A rectangle has a width six less than the length. The perimeter is 16 inches. Write the equation if the length = x. Find the dimensions of the rectangle.

Answer 1

The length of the rectangle is 7 inches and the width is 1 inch, where the width is six inches less than the length, and the perimeter of the rectangle is 16 inches.

Step-by-step explanation:

The student is asked to find the dimensions of a rectangle where the width is six inches less than the length and the perimeter is 16 inches. First, let's define the length of the rectangle as x inches. Then, the width will be x - 6 inches because the width is six less than the length. Since the formula for the perimeter (P) of a rectangle is P = 2(length) + 2(width), we write the equation as 16 = 2x + 2(x - 6).

To find the dimensions, we solve for x:

1. Distribute the 2: 16 = 2x + 2x - 12
2. Combine like terms: 16 = 4x - 12
3. Add 12 to both sides: 28 = 4x
4. Divide both sides by 4: x = 7

Now we can find the width:

Width = x - 6 = 7 - 6 = 1 inch.

The dimensions of the rectangle are therefore 7 inches by 1 inch.