A triangle has a perimeter of $4$ [i]yards[/i] and an area of $6$ square [i]feet[/i].  If one of the angles of the triangle is right, what is the length of the largest side of the triangle, in feet?

[i]2016 CCA Math Bonanza Lightning #1.4[/i]
1. **Convert the perimeter from yards to feet:**
   \[
   4 \text{ yards} = 4 \times 3 = 12 \text{ feet}
   \]
   This is because 1 yard = 3 feet.

2. **Identify the relationship between the area and the legs of the right triangle:**
   Given that the area of the triangle is 6 square feet, and one of the angles is a right angle, we can use the formula for the area of a right triangle:
   \[
   \text{Area} = \frac{1}{2} \times \text{leg}_1 \times \text{leg}_2
   \]
   Substituting the given area:
   \[
   6 = \frac{1}{2} \times \text{leg}_1 \times \text{leg}_2
   \]
   Solving for the product of the legs:
   \[
   \text{leg}_1 \times \text{leg}_2 = 12
   \]

3. **Determine the possible integer values for the legs:**
   We need to find pairs of integers whose product is 12. The pairs are:
   \[
   (1, 12), (2, 6), (3, 4)
   \]
   However, we need to ensure that the perimeter condition is also satisfied.

4. **Check the perimeter condition:**
   The perimeter of the triangle is given as 12 feet. For a right triangle, the perimeter is the sum of the two legs and the hypotenuse. Using the Pythagorean theorem, the hypotenuse \( c \) is given by:
   \[
   c = \sqrt{\text{leg}_1^2 + \text{leg}_2^2}
   \]
   We need to check which pair of legs satisfies the perimeter condition:
   - For \((1, 12)\):
     \[
     \text{Hypotenuse} = \sqrt{1^2 + 12^2} = \sqrt{1 + 144} = \sqrt{145}
     \]
     Perimeter:
     \[
     1 + 12 + \sqrt{145} \neq 12
     \]
   - For \((2, 6)\):
     \[
     \text{Hypotenuse} = \sqrt{2^2 + 6^2} = \sqrt{4 + 36} = \sqrt{40}
     \]
     Perimeter:
     \[
     2 + 6 + \sqrt{40} \neq 12
     \]
   - For \((3, 4)\):
     \[
     \text{Hypotenuse} = \sqrt{3^2 + 4^2} = \sqrt{9 + 16} = \sqrt{25} = 5
     \]
     Perimeter:
     \[
     3 + 4 + 5 = 12
     \]
     This pair satisfies the perimeter condition.

5. **Identify the largest side:**
   The largest side in a right triangle is the hypotenuse. For the pair \((3, 4)\), the hypotenuse is 5 feet.

The final answer is \(\boxed{5}\) feet.