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rafeds08

  • 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?

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  1. rafeds08
    • 3 years ago
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    |dw:1349246075538:dw|

  2. JakeV8
    • 3 years ago
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    wow, that's not too easy, is it?

  3. rafeds08
    • 3 years ago
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    yes

  4. TheMind
    • 3 years ago
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    not enough info

  5. JakeV8
    • 3 years ago
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    |dw:1349246702016:dw|

  6. JakeV8
    • 3 years ago
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    that geometry could give you a radius of the larger square, if you knew anything at all about the dimensions or area

  7. JakeV8
    • 3 years ago
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    sorry, not "radius of square" (it's late) diagonal of square = radius of circle

  8. hartnn
    • 3 years ago
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    |dw:1349246849703:dw|

  9. JakeV8
    • 3 years ago
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    I stand ready to be wow'd... please continue...

  10. hartnn
    • 3 years ago
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    i mean thats the info needed to be given, then u can find the area

  11. JakeV8
    • 3 years ago
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    ok, I'm with you on that...

  12. JakeV8
    • 3 years ago
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    I thought you were about to pull some geometry magic...

  13. JakeV8
    • 3 years ago
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    expectations run high, ya know...

  14. akash_809
    • 3 years ago
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    |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. akash_809
    • 3 years ago
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    @rafeds08 solve the above equations to get the answer

  16. JakeV8
    • 3 years ago
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    I haven't solved, but that appears logical... well done :)

  17. akash_809
    • 3 years ago
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    thanks @JakeV8 , i haven't solved it either but i think solving these equations will give the answer

  18. JakeV8
    • 3 years ago
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    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. akash_809
    • 3 years ago
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    |dw:1349249269180:dw| which symbol can u point it out....

  20. akash_809
    • 3 years ago
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    @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. JakeV8
    • 3 years ago
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    never mind :) I just realized it's the label "r" on the second radius... my oops!

  22. akash_809
    • 3 years ago
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    @rafeds08 did u get the answer on solving the above equations

  23. rafeds08
    • 3 years ago
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    they told me its 64

  24. rafeds08
    • 3 years ago
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    thus radius of big circle is 8

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