Question

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

Answer 1

x = 9/2

Explanation:

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

The missing side can be calculated with pythagoras as:

`√(8^2-6^2) = √(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`