Question

Hey can someone please give me a step by step explian the answer

Answer 1

Answer:

x = 9/2

Step-by-step explanation:

The outside triangle is also a right triangle, with hypotenuse 8 and side 6.

The missing side can be calculated with pythagoras as:

$\sqrt{8^2-6^2} = \sqrt{28}$

Now for the vertical line, lets call it y, which is a side for two "back to back" triangles, you can do pythagoras twice:

left triangle: $y^2 + (8-x)^2 = 28$

right triangle: $y^2 + x^2 = 6^2$

Eliminating y², you can solve:

$28 - (8-x)^2 = 36 - x^2$

$28 -x^2 + 16x - 64 = 36 - x^2$

$16x = 36 + 64 - 28$

$x = \frac92$