Question

Will give brainliest

Answer 1

Answer:

25.047 or roughly 25.

Step-by-step explanation:

I solved it wrong the first time then i double check with wolframalpha and got the correct number.

We know that the area of the tile is 18 $\sqrt{3}$ and it makes a triangle, we also know the base and height. In this case the base is 2$\sqrt{3}^{x/12}$ and the height is also given which is $\sqrt{3}^{\frac{x}{6} }$.

Area of triangle = $\frac{bh}{2}$,

substituting we will end up with  18 $\sqrt{3}$  =( 2$\sqrt{3}^{x/12}$  *  $\sqrt{3}^{\frac{x}{6} }$) / 2

Here is the tricky part $\sqrt{x} = x^{\frac{1}{2} }$, i totally forgot about that lol.

Simplifying: we will get  18 $\sqrt{3}$ = $3^{\frac{x}{8} }$

Now, in order to find the x, we will need to take the log of both sides.

$log18\sqrt{3} = \frac{x}{8} log3$

Solving for x we end up getting:

$8\frac{log18\sqrt{3} }{log3}$ = x

where x = 25.047.

To be honest I deserve a nobel prize not a brainliest lol.

Good question bro, take it easy.