Please help ! i need help with my geometry homework

Step-by-step explanation:

We have three right triangles

For the biggest one from Pythagoras Theorem the square of its base side length (let it be a) is:

                                    a² = (x+7)² - 12²

The square of the segment inside the biggest triangle (let it be h) is:

From the smallest triangle: h² = a² - 7²

From the medium triangle:  h² = 12² - x²

Therefore:

               a² - 7² = 12² - x²

   (x+7)² - 12²  - 7² = 12² - x²

x² + 2·x·7 + 7² - 12²  - 7² = 12² - x²

x² + 14x - 144 = 144 - x²

x² + x² + 14x -144 - 144 = 0

2x² + 14x - 288 = 0        

 x² + 7x - 144 = 0

{ <0, so is not apllicable}

a is the correct

step-by-step explanation: