## highschoolmom2010 2 years ago What is the side length of the smallest square plate on which a 20-cm chopstick can fit along a diagonal without any overhang? Round your answer to the nearest tenth of a centimeter.

1. dumbcow

use fact the diagonal of a square is sqrt2 times side length |dw:1375640019150:dw|

2. highschoolmom2010

|dw:1375640072724:dw|

3. highschoolmom2010

is that how i need to set it up?

4. gypsy1274

Looks good to me. Do you know where to go from there?

5. highschoolmom2010

eh not really well ....

6. gypsy1274

I would use the pythagorean theorem to find the length of the sides. Does that help?

7. highschoolmom2010

so x^2+x^2=20^2 x^2+x^2=400^@

8. gypsy1274

Before taking the square root, divide both sides by 2.

9. gypsy1274

$$x^2+x^2 = 20^2$$ $$2x^2=400$$

10. dumbcow

haha ok i guess you didn't get my drawing...you could just say $\sqrt{2} x = 20$ $x = \frac{20}{\sqrt{2}}$

11. highschoolmom2010

oh ok $\frac{ 2x^2 }{ 2 }=\frac{ 400 }{ 2 }$ $x^2=200$ $\sqrt{x^2}=\sqrt{200}$

12. highschoolmom2010

|dw:1375640872842:dw| what do i do from here

13. gypsy1274

Yes, that would be great if you were supposed to have a radical in your answer, but your question says to round to the nearest tenth, so use a calculator (or google) to get the square root of 200.

14. dumbcow

they want answer as decimal so no point in simplifying radical ...

15. dumbcow

haha:)

16. gypsy1274

You might want to save @dumbcow's original picture and equation to spend a rainy day in contemplation. If you can remember it the next time you need it, that would be a quicker way of getting to the answer.

17. highschoolmom2010

well if i needed the simple radical i was headed right :DD

18. highschoolmom2010

$\approx 14.14$

19. gypsy1274

Yes, you simplified the radical very well. And in later classes, you will probably need to leave your answer like that. Rounded to the nearest tenth is one place after the decimal....

20. highschoolmom2010

$\approx14$

21. highschoolmom2010

sorry i forgot that for a second

22. gypsy1274

$$\approx14.1$$

23. highschoolmom2010

oh well i got that all mixed up

24. gypsy1274

You did well.

25. highschoolmom2010

ty @gypsy1274 & @dumbcow

26. gypsy1274