## anonymous 3 years ago Two squares are inscribed in a semicircle, as shown. The area of the smaller square is 16. What is the area of the larger square?

1. anonymous

|dw:1349246075538:dw|

2. anonymous

wow, that's not too easy, is it?

3. anonymous

yes

4. anonymous

not enough info

5. anonymous

|dw:1349246702016:dw|

6. anonymous

that geometry could give you a radius of the larger square, if you knew anything at all about the dimensions or area

7. anonymous

sorry, not "radius of square" (it's late) diagonal of square = radius of circle

8. hartnn

|dw:1349246849703:dw|

9. anonymous

10. hartnn

i mean thats the info needed to be given, then u can find the area

11. anonymous

ok, I'm with you on that...

12. anonymous

I thought you were about to pull some geometry magic...

13. anonymous

expectations run high, ya know...

14. anonymous

|dw:1349248195417:dw| i hope the following figure solves it , let y be the length of side of big square, then $r=\sqrt{y^2+(y^2/4)}$ and also from the other traingle $r=\sqrt { 16+(4+y/2)^2 }$ equate both the equations and solve for y ,and ares of bigger square is y^2

15. anonymous

@rafeds08 solve the above equations to get the answer

16. anonymous

I haven't solved, but that appears logical... well done :)

17. anonymous

thanks @JakeV8 , i haven't solved it either but i think solving these equations will give the answer

18. anonymous

I agree... good eye to see another way to define "r". Nitpick... looks like you drew a right angle symbol on the inside of the larger triangle with sides r, y, and y/2, situated along the other radius line drawn toward the smaller circle. This appears misplaced, or the symbol is something else, or I don't get it (option c is always a good guess)... Can you explain?

19. anonymous

|dw:1349249269180:dw| which symbol can u point it out....

20. anonymous

@JakeV8 i just used the orignal diagram, but icant seem to find the symbol u r talking abt, to me it clearly looks that both the triangles are right angled.

21. anonymous

never mind :) I just realized it's the label "r" on the second radius... my oops!

22. anonymous

@rafeds08 did u get the answer on solving the above equations

23. anonymous

they told me its 64

24. anonymous

thus radius of big circle is 8