Question

Find x of the triangle

Answer 1

3.875

Explanation:

A lot of Pythagorean theorem stuff!

First, find the base of the biggest triangle:

`6^2+b^2=8^2\\36+b^2=64\\b^2=28\\b=√(28)`

Next up, find the base of the second biggest triangle:

`a^2+(8-x)^2=(√(28))^2\\a^2+64-16x+x^2=28 \\a^2=-36+16x-x^2\\a=√(-36+16x-x^2)`

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:

`(√(-36+16x-x^2))^2+x^2=6^2\\-36+16x-x^2+x^2=36\\16x=62\\x=3.875`

And we are done!... or not...?

We still need to go back to the second equation to make sure everything is positive:

`a=√(-36+16x-x^2)\\a=√(-36+16(3.875)-(3.875)^2)\\a=√(-36+62-15.015625) \\a=√(10.984375)`

Whew, thankfully everything is positive.

Now for the second time, we are now done.