As Randi starts to solve for $x$ in the diagram at right, she writes the equation $7^2 + x^2 = (x + 1)^2$.

1. Is Randi’s equation valid? Explain your thinking.

   Hint (a):

   Notice the right angle.

   Answer (a):

   Yes, she used the Pythagorean Theorem.

2. What is the perimeter of Randi’s triangle?

   Hint (b):

   Once you solve the equation you will need to use the value of $x$ to determine the length of each side of the triangle.