Answer:
Width = 60 inches
Length = 76 inches
Explanation:
We can find the rectangle's length and width using a system of equations, where:
- L represents length,
- and the W represent width.
First equation:
Since the rectangle's length is 16 inches more than its width, our first equation is given by:
L = W + 16
Second equation:
The formula for the perimeter of a rectangle is given by:
P = 2L + 2W, where:
- P represents the perimeter,
- L represents the length,
- and W represents the width.
Since the rectangle's perimeter is 272 inches, our second equation is given by:
272 = 2L + 2W
Method to solve: Substitution:
Solving for W:
We can solve for W by substituting W + 16 for L in the second equation (i.e., 272 = 2L + 2W):
272 = 2(W + 16) + 2W
272 = 2W + 32 + 2W
(272 = 4W + 32) - 32
(240 = 4W) / 4
60 = W
Thus, the rectangle's width is 60 inches.
Solving for L:
Now, we can solve for L by plugging in 60 for W in the second first equation (i.e., L = W + 16):
L = 60 + 16
L = 76
Thus, the rectangle's length is 76 inches.