Geometry problems ...

[Axtremus]

My solution to Variation-A:

The black outline polygon ABCDE is the information provided in the problem.

• Use the information from the BCDE line segments to construct the BF(D)E triangle.
• Realize that the BAE triangle is congruent to the BFE triangle.
• Hence the length of FE equals the length of AE, x = 8

[Axtremus]

My solution for Variation-B, as mentioned before, need to apply the Pythagorean Theorem twice, but it is essentially the same as already described by @Horace (4 posts above, and 6 posts above).

Some one made YouTube video that very nicely illustrated that solution:

Link to video

I got these two problems from that YouTube video.

[Horace]

In fairness, I also anticipated what your solution to variation A was, in my last post.

[Klaus]

That was a nice puzzle. Initially I made it way more complicated than it needed to be. I'm a little proud I found a solution that doesn't require Pythagoras or, for that matter, any formula at all