Question

The length of a rectangle is 4 centimeters less than twice it’s width. The perimeter of the rectangle is 34vm. What are the dimensions of the rectangle?

Answer 1

To begin to solve this question, we need to express the lengths in terms of width of the width in terms of length. Since the question says that the length was 4 centimeters less than twice the width, that means that the length is equal to 4 centimeters less (minus) twice the width (times two). That means that l = 2w - 4. We also know that the perimeter is 34cm.

The formula for the area of a rectangle is 2l + 2w, or 2(2w - 4) + 2w. Since the perimeter is 34, that means that:

4w - 8 + 2w = 34

Combining like terms and moving the numbers to the other side, we get:

6w = 42

w = 7

Plugging in the value of w in the formula for the length, we get that l = 2 (7) - 4 = 14 - 4 = 10. That means that the correct answer is C.

Answer 2

l = 2w - 4

Because we're solving for 2l + 2w, that can be simplified to

2(2w - 4) + 2w = 34

4w - 8 + 2w = 34

6w - 8 = 34

6w = 42

w = 7

Knowing this, we can input w:

2(7) + 2l = 34

14 + 2L = 34

2l = 20

l = 10

L = 10, W = 7, Option C