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janessia

  • 2 years ago

Find the perimeter of the triangle at the right. Assume that the line segments are tangent to the circle.

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  1. janessia
    • 2 years ago
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  2. janessia
    • 2 years ago
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    @jim_thompson5910

  3. janessia
    • 2 years ago
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    @MathLegend

  4. jim_thompson5910
    • 2 years ago
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    if you cut the figure up like this |dw:1353204276912:dw|

  5. janessia
    • 2 years ago
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    mmmhhhmmm

  6. jim_thompson5910
    • 2 years ago
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    you'll see that 2 triangles form

  7. janessia
    • 2 years ago
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    yes

  8. jim_thompson5910
    • 2 years ago
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    namely, the smaller triangles inside the larger ones

  9. jim_thompson5910
    • 2 years ago
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    highlighted here|dw:1353204485777:dw|

  10. janessia
    • 2 years ago
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    ohk

  11. jim_thompson5910
    • 2 years ago
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    so if we know this |dw:1353204546161:dw|

  12. jim_thompson5910
    • 2 years ago
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    then we can say this as well |dw:1353204577254:dw|

  13. janessia
    • 2 years ago
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    ohk yes i see that

  14. janessia
    • 2 years ago
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    so then can we say that the other side is 9 as well?

  15. jim_thompson5910
    • 2 years ago
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    let me think, I'm looking for justification that the two larger triangles are congruent

  16. janessia
    • 2 years ago
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    ohk

  17. jim_thompson5910
    • 2 years ago
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    oh wait, not sure why i didn't see this til now lol

  18. jim_thompson5910
    • 2 years ago
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    |dw:1353204871377:dw|

  19. jim_thompson5910
    • 2 years ago
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    the smaller two triangles in the lower right corner are isosceles triangles

  20. jim_thompson5910
    • 2 years ago
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    you have to draw another line to see this if you can't

  21. jim_thompson5910
    • 2 years ago
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    so that's why we can add the extra 9 on there the 6 comes from the fact that 9+6 = 15

  22. jim_thompson5910
    • 2 years ago
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    so to finish things off, we get this full picture |dw:1353204976827:dw|

  23. janessia
    • 2 years ago
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    ohk why did u choose 9 and 6... those arent the only things that add together to get 15

  24. jim_thompson5910
    • 2 years ago
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    yes, but the 9 is locked in, which is why the second segment has to be a 6

  25. jim_thompson5910
    • 2 years ago
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    if you don't see what I mean, go back to a previous drawing where I show how the second 9 (the lower 9) shows up

  26. janessia
    • 2 years ago
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    i get it so 58 is the answer

  27. jim_thompson5910
    • 2 years ago
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    yep

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