what is the length of a diagonal of a cube with side x

Question

shadowfiend · Answer

If you draw a diagonal, what two shapes do you get in the square?

anonymous · Answer

2 triangles

shadowfiend · Answer

Right. Are they a particular kind of triangle?

anonymous · Answer

a right triangle

anonymous · Answer

so how do i sole the problem

anonymous · Answer

slove*

shadowfiend · Answer

Sorry. So, you have a right triangle, and the two sides that are not the hypotenuse are of length x. Do you have an equation that will let you calculate the length of the hypotenuse?

anonymous · Answer

a suared + b squared + c squared ?

shadowfiend · Answer

$a^2 + b^2 = c^2$, right, the Pythagorean theorem. So plug it in and solve for c :)

anonymous · Answer

thank you so its going to be 2^ +  ? + C^ kinda lost again

anonymous · Answer

x (root3)

anonymous · Answer

whats the problem going to look ike and the answer please

anonymous · Answer

helllo

shadowfiend · Answer

Yikes, sorry.

So if you plug x in, you get:

$$\begin{align}
x^2 + x^2 &= c^2\
2x^2 &= c^2
\end{align}$$
We can then take the square root of both sides:

$$\begin{align}
2x^2 &= c^2\
\sqrt{2x^2} &= c\
x\sqrt{2} = c
\end{align}$$

And that's it!

anonymous · Answer

thank you

shadowfiend · Answer

No problem. Click `good answer' next to my answer :)