Question

HOW DO I SOLVE THIS HELP

Answer 1

`x=2\sqrt5`

Explanation:

I'm assuming that 15 is the length of only part of the hypotenuse of the larger triangle.

The remaining part can be easily found by noticing that the red triangle is half an equilateral triangle of side x, so the missing part is x/2.

Now for a known theorem (easily proved with the fact that triangles AHC and ABC are similar) you can write the following equation containing x:

`x^2 = \frac x2 ( \frac x2 +15) \rightarrowx^2 = \frac {x^2}4+15 \\\\3x^2=60 \rightarrow x^2 = 20 \\x=2\sqrt5`

(where we obviously took only the positive root since x is a lengtth measure.