Theo is building a garden against his house. He bought two pieces of wood that are each five feet long. He wants to create a triangular garden against his house using the two pieces of wood, without cutting them. His house will be the third side of the triangle. He also wants the perimeter of his garden to be a whole number.
In order for the perimeter to be a whole number, the two pieces of wood must be able to form a right triangle with the house as the third side. This means that the two pieces of wood must satisfy the Pythagorean theorem, which states that a^2 + b^2 = c^2, where c is the hypotenuse (the side opposite the right angle).
Since each piece of wood is 5 feet long, we can let one side of the triangle be 5 feet (let's call this side "a") and the other side be the other 5-foot piece of wood (let's call this side "b"). To find the length of the house side (c), we can use the Pythagorean theorem:
5^2 + 5^2 = c^2
25 + 25 = c^2
50 = c^2
c = √50
c ≈ 7.07 feet
Therefore, the length of the house side must be approximately 7.07 feet in order for the perimeter to be a whole number.