Answer:
x = 9
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
[tex]a=1\,,\ b=7\,,\ c=-144\\\\\bold{x=\dfrac{-7\pm\sqrt{7^2-4\cdot1\cdot(-144)}}{2\cdot1}=\dfrac{-7\pm\sqrt{49+576}}{2}=\dfrac{-7\pm\sqrt{625}}2}[/tex]
[tex]\bold{x=\dfrac{-7+25}{2}=9}[/tex]
{[tex]x=\frac{-7-25}{2}=-16[/tex] <0, so is not apllicable}
