## anonymous 5 years ago what is the length of a diagonal of a cube with side x

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

2. anonymous

2 triangles

Right. Are they a particular kind of triangle?

4. anonymous

a right triangle

5. anonymous

so how do i sole the problem

6. anonymous

slove*

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?

8. anonymous

a suared + b squared + c squared ?

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

10. anonymous

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

11. anonymous

x (root3)

12. anonymous

13. anonymous

helllo

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!

15. anonymous

thank you