Answer:
Width = 13 centimeters
Explanation:
Formula for the perimeter of a rectangle:
The formula for the perimeter of a rectangle is given by:
P = 2L + 2W, where
- P is the perimeter,
- L is the length,
- and W is the width.
Equation relating the length and width:
Since the rectangle's length 5 cm longer than twice its width, we can represent this with the following equation:
L = 2W + 5
Finding the width:
Since the perimeter is 88 cm, we can find the width by substituting 88 for P and 2W + 5 for L in the rectangle perimeter formula:
88 = 2(2W + 5) + 2W
88 = 4W + 10 + 2W
(88 = 6W + 10) - 10
(78 = 6W) / 6
13 = W
Thus, the rectangle's width is 13 centimeters.
Optional: Find the length to check the validity of the answer:
Since the length is 5 cm more than twice the width, the length is 31 centimeters as (2 * 13) + 5 = 31.
Now we can substitute 88 for P, 31 for L and 13 for W in the rectangle perimeter formula and check whether we get 88 on both sides of the equation:
88 = 2(31) + 2(13)
88 = 62 + 26
88 = 88
Thus, our answer for the width is correct.