Final answer:
To find the length and width of the rectangle, we can set up equations based on the given information and solve them simultaneously. The length is 43.25 inches and the width is 14.75 inches.
Step-by-step explanation:
To solve this problem, we can start by setting up equations based on the given information:
We are told that the length(L) of the rectangle is one less than three times the width(W).
So we can write the equation: L = 3W - 1.
We are also given that the perimeter of the rectangle is 116 inches.
The formula for finding the perimeter is P = 2L + 2W, so we can write the equation: 2L + 2W = 116.
Now we can solve these equations simultaneously to find the values of L and W:
Substitute the equation for L into the second equation: 2(3W - 1) + 2W = 116.
Simplify and solve for W: 6W - 2 + 2W = 116. 8W = 118. W = 118/8 = 14.75.
Substitute the value of W back into the equation for L: L = 3(14.75) - 1 = 44.25 - 1 = 43.25.
So the length of the rectangle is 43.25 inches and the width is 14.75 inches.