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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?
 one year ago
 one year 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?
 one year ago
 one year ago

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xRAWRRx3Best ResponseYou've already chosen the best response.0
dw:1338703391644:dw
 one year ago

jim_thompson5910Best ResponseYou've already chosen the best response.1
Are you familiar with any trig?
 one year ago

jim_thompson5910Best ResponseYou've already chosen the best response.1
hmm then again, you said geometry, so let me think of a way to do it without trig
 one year ago

xRAWRRx3Best ResponseYou've already chosen the best response.0
no no, you can use a bit of trig if it is simple :)
 one year ago

jim_thompson5910Best ResponseYou've already chosen the best response.1
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
 one year ago

jim_thompson5910Best ResponseYou've already chosen the best response.1
Step 2) Cut TD in half. Label the midpoint of TD point F and draw the segment EF dw:1338704102241:dw
 one year ago

jim_thompson5910Best ResponseYou've already chosen the best response.1
The length of TF and FD are x/2 since we've cut TD = x in half
 one year ago

jim_thompson5910Best ResponseYou've already chosen the best response.1
FE = TB, so FE = 10
 one year ago

jim_thompson5910Best ResponseYou've already chosen the best response.1
So we have the following dw:1338704182291:dw
 one year ago

jim_thompson5910Best ResponseYou've already chosen the best response.1
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.
 one year ago

jim_thompson5910Best ResponseYou've already chosen the best response.1
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
 one year ago

xRAWRRx3Best ResponseYou've already chosen the best response.0
thank you so much x) you really helped me x)
 one year ago
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