Final answer:
The length of a rectangle with a perimeter of 192ft and a length three times its width is 72ft. We find this by first deriving the width from the given perimeter and then using the relationship between length and width.
Step-by-step explanation:
To find the length of a rectangle when given the perimeter and the relationship between length and width, we use the formula P = 2l + 2w. In this instance, the perimeter (P) is given as 192ft. The problem also states that the length (l) is three times longer than the width (w), which translates to l = 3w. Substituting l for 3w in the perimeter formula, we get:
P = 2(3w) + 2w
This simplifies to P = 6w + 2w, which is the equivalent of P = 8w. Dividing both sides of the equation by 8 to solve for w, we find:
w = P/8
Substituting the known perimeter value,
w = 192ft / 8
w = 24ft
Knowing the width and the length's relation to the width, we calculate the length:
l = 3w = 3(24ft) = 72ft
Therefore, the length of the rectangle is 72 feet.