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xRAWRRx3

  • 3 years ago

Please help :( In the figure below, triangle TED in rectangle TBCD is equilateral. If TB = 10, to the nearest hundredth, what is the length of ED?

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  1. xRAWRRx3
    • 3 years ago
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    |dw:1338703391644:dw|

  2. jim_thompson5910
    • 3 years ago
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    Are you familiar with any trig?

  3. xRAWRRx3
    • 3 years ago
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    well, a little bit.

  4. jim_thompson5910
    • 3 years ago
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    hmm then again, you said geometry, so let me think of a way to do it without trig

  5. xRAWRRx3
    • 3 years ago
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    no no, you can use a bit of trig if it is simple :)

  6. jim_thompson5910
    • 3 years ago
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    Step 1) Label the length of ED x. So TE = x and TD = x as well since we're dealing with an equilateral triangle |dw:1338704023305:dw|

  7. jim_thompson5910
    • 3 years ago
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    Step 2) Cut TD in half. Label the midpoint of TD point F and draw the segment EF |dw:1338704102241:dw|

  8. jim_thompson5910
    • 3 years ago
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    The length of TF and FD are x/2 since we've cut TD = x in half

  9. jim_thompson5910
    • 3 years ago
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    FE = TB, so FE = 10

  10. jim_thompson5910
    • 3 years ago
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    So we have the following |dw:1338704182291:dw|

  11. jim_thompson5910
    • 3 years ago
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    Since we have the right triangle EFD, we can say EF^2 + FD^2 = ED^2 but we know that EF = 10, FD = x/2 and ED = x, so... 10^2 + (x/2)^2 = x^2 100 + x^2/4 = x^2 400 + x^2 = 4x^2 400 = 4x^2 - x^2 400 = 3x^2 3x^2 = 400 x^2 = 400/3 x = sqrt(400/3) x = 20/sqrt(3) x = 20*sqrt(3)/3 So the exact length of ED is 20*sqrt(3)/3 units.

  12. jim_thompson5910
    • 3 years ago
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    After that, use a calculator to get 20*sqrt(3)/3 = (20*1.73205)/3 = 34.641/3 = 11.547 Giving us that ED is approximately 11.547 units, which rounds to 11.55

  13. xRAWRRx3
    • 3 years ago
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    thank you so much x) you really helped me x)

  14. jim_thompson5910
    • 3 years ago
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    yw

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