Final answer:
Using the given perimeter and the relationship between the rectangle's length and width, we calculated the width to be 21 inches and subsequently found the length to be 66 inches.
Step-by-step explanation:
Finding the Length of a Rectangle
The question involves finding the length of a rectangle given its perimeter and a relationship between its length and width. We are told that the length (L) is 3 more than 3 times its width (W), which we can express as L = 3W + 3. The perimeter (P) of the rectangle is given as 174 inches, and the formula for the perimeter of a rectangle is P = 2L + 2W. Substituting the expression for L into the perimeter formula, we get:
174 = 2(3W + 3) + 2W
We simplify this equation as follows:
174 = 6W + 6 + 2W
174 = 8W + 6
168 = 8W (after subtracting 6 from both sides)
W = 21 (after dividing both sides by 8)
Now that we know the width is 21 inches, we can find the length by substituting W back into the first equation:
L = 3(21) + 3 = 63 + 3 = 66 inches
The length of the rectangle is therefore 66 inches.