## 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?

1. xRAWRRx3

|dw:1338703391644:dw|

2. jim_thompson5910

Are you familiar with any trig?

3. xRAWRRx3

well, a little bit.

4. jim_thompson5910

hmm then again, you said geometry, so let me think of a way to do it without trig

5. xRAWRRx3

no no, you can use a bit of trig if it is simple :)

6. jim_thompson5910

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

Step 2) Cut TD in half. Label the midpoint of TD point F and draw the segment EF |dw:1338704102241:dw|

8. jim_thompson5910

The length of TF and FD are x/2 since we've cut TD = x in half

9. jim_thompson5910

FE = TB, so FE = 10

10. jim_thompson5910

So we have the following |dw:1338704182291:dw|

11. jim_thompson5910

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

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

thank you so much x) you really helped me x)

14. jim_thompson5910

yw