Answer:
3.875
Step-by-step explanation:
A lot of Pythagorean theorem stuff!
First, find the base of the biggest triangle:
[tex]6^2+b^2=8^2\\36+b^2=64\\b^2=28\\b=\sqrt{28}[/tex]
Next up, find the base of the second biggest triangle:
[tex]a^2+(8-x)^2=(\sqrt{28})^2\\a^2+64-16x+x^2=28 \\a^2=-36+16x-x^2\\a=\sqrt{-36+16x-x^2}[/tex]
At the moment we still don't know x, so we will later need to come back to make sure that this expression is positive.
Next up, the smallest triangle:
[tex](\sqrt{-36+16x-x^2})^2+x^2=6^2\\-36+16x-x^2+x^2=36\\16x=62\\x=3.875[/tex]
And we are done!... or not...?
We still need to go back to the second equation to make sure everything is positive:
[tex]a=\sqrt{-36+16x-x^2}\\a=\sqrt{-36+16(3.875)-(3.875)^2}\\a=\sqrt{-36+62-15.015625} \\a=\sqrt{10.984375}[/tex]
Whew, thankfully everything is positive.
Now for the second time, we are now done.
