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.
