As Randi started to solve for $x$ in the diagram at right, she wrote 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. To solve her equation, first rewrite $(x+1)^2$ by multiplying $(x+1)(x+1)$. You may want to review the Math Notes box for Lesson 2.2.2.

3. Now solve your equation for $x$.

   Hint (c):

   Use a generic rectangle to multiply the binomials.

   Answer (c):

   $x=24$

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

   Hint (d):

   Use the value of $x$ to determine the length of each side of the triangle.