+0  
 
0
40
1
avatar

In right triangle ABC, angle B=90 degrees, and D and E lie on AC such that \(​​​​\overline{BD}\) is a median and \(\overline{BE}\)  is an altitude. If BD=2 x DE, compute \(\frac{AB}{EC}\).

Guest Aug 21, 2018
 #1
avatar+343 
+1

\(\Delta DEB\)  is a \(30 - 60 - 90\) triangle, so \(BE = \sqrt{3}(DE)\)\(EC = DE\), and since we are only looking for ratios, we can assign \(DE\) and \(EC\) to \(x\)\(\Delta ABC\) is a \(30 - 60 - 90\) triangle also. \(AC\) is \(4x\) because \(BD\) is a median, therefore splitting \(AC\) into two. Since \(AC = 4x\)\(BC = 2x\). (If you didn't know already, a \(30 - 60 - 90\) triangle's sides are in a ratio of \(1 : \sqrt{3} : 2\).) If \(BC = 2x\), then \(AB = 2\sqrt{3}x\), and \(EC = x\), so your ratio would be \(\frac{2\sqrt{3}x}{x}\), which simplifies to \(2\sqrt{3}\) when you cancel the \(x\)'s.

 

- Daisy

dierdurst  Aug 22, 2018

4 Online Users

New Privacy Policy

We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive information about your use of our website.
For more information: our cookie policy and privacy policy.