What is the value of x in the figure below? Show your work.

Answer:2√26Step-by-step explanation:First, let's label side AB as y and side BP as h.Then, using the Pythagorean Theorem, we can determine that for ΔABP, 5²+h²=y², which is equal to h² = y²- 25.For ΔBPC, 8²+ h² = x², which is equal to h² = x²- 64.Because both equations are equal to h², you can determine that y²- 25 = x²- 64. You can rewrite this equation as x²- y² = 39.Then, for ΔABC, x²+ y² = (5+8)², which is equal to x²+ y² = 169.Now, you can see that we have a system of equations. Using elimination, we can add the equations, getting:2x² = 208x² = 104x = ±√104 which simplifies into ±2√26, but since x is a distance, and distance is always positive, the answer has to be 2√26.