Question

Solve for the missing side: simplify the radical ​

Answer 1

Answer:

$x=8\sqrt{5}$

Step-by-step explanation:

I will assume the following:

• You know how to use  the quadratic formula
• You know how to simplify radicals
• You know how to use the pythagorean theorem.

The challenge of this exercise comes from using the pythagorean theorem and setting up a few equations.

Given that we have a segment 36 units long and another segment that is 16, it is trivial to get the other segment, 20. Additionally, there are two sides that I want to name so that way I can make a couple of substitutions. I will call these side a and side b. (see attachment 1)

Now comes with setting up three equations. I will start with the two smaller triangles, using side a and side b. See attachments 2 and 3.

Now with the big triangle. I will set up one last equation. See attachment 4.

Given what we know about attachment 2 and 3, we can make two substitutions. See attachment 5. I assume you know how to do the rest and arrive at your only real solution.