What is the largest perimeter possible for a rectangle with positive whole-number dimensions and an area of 80 square centimeters?
Let's assume the dimensions of the rectangle are length (L) and width (W) in centimeters.
The area (A) of a rectangle is given by the formula A = L * W.
Given that the area is 80 square centimeters, we have the equation 80 = L * W.
To find the largest possible perimeter, we need to maximize the sum of the length and width. Let's consider a few scenarios:
1. L = 1 and W = 80: In this case, the perimeter would be 2 * (1 + 80) = 162.
2. L = 2 and W = 40: Here, the perimeter would be 2 * (2 + 40) = 84.
3. L = 4 and W = 20: The perimeter, in this case, would be 2 * (4 + 20) = 48.
4. L = 5 and W = 16: With these dimensions, the perimeter would be 2 * (5 + 16) = 42.
5. L = 8 and W = 10: In this scenario, the perimeter would be 2 * (8 + 10) = 36.
Observing the above cases, we can see that the largest perimeter occurs when L = 2 and W = 40, resulting in a perimeter of 84 centimeters.