We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website. cookie policy and privacy policy.
 
+0  
 
+1
187
1
avatar

We have a triangle \(\triangle ABC\) and a point \(K\) on segment \(\overline{BC}\) such that \(AK\) is an altitude to \(\triangle ABC\). If \(AK = 6,\) \(BK = 8\), and \(CK = 6,\) then what is the perimeter of the triangle?

 Dec 18, 2018

Best Answer 

 #1
avatar+7531 
+2

First thing we know BC = BK + CK = 14.

Then we use Pythagorean theorem twice to get:

\(AB = \sqrt{AK^2 + BK^2} = 10\)

\(AC = \sqrt{AK^2+CK^2} = 6\sqrt2\)

Therefore,

Perimeter = AB + AC + BC = 14 + 10 + 6√2 = 24 + 6 √ 2

 Dec 18, 2018
 #1
avatar+7531 
+2
Best Answer

First thing we know BC = BK + CK = 14.

Then we use Pythagorean theorem twice to get:

\(AB = \sqrt{AK^2 + BK^2} = 10\)

\(AC = \sqrt{AK^2+CK^2} = 6\sqrt2\)

Therefore,

Perimeter = AB + AC + BC = 14 + 10 + 6√2 = 24 + 6 √ 2

MaxWong Dec 18, 2018

19 Online Users

avatar
avatar