☆Be right in right triangle....
Geometry
Level
1
In right triangle ABC , right angled at B ,the sides forming the right angle are a&b a+b=7&ab=a+b+5. BX is median on AC. Find BX.
The answer is 2.5.
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1 solution
a + b = 7 , a b = 1 2 ⇒ a 2 + b 2 = ( a + b ) 2 − 2 a b = 2 5 Hence the sides are 3 , 4 , 5 . Using Apollonius theorem, A B 2 + B C 2 = 2 ( B X 2 + X A 2 ⇒ B X = 2 2 5 − 2 • ( 2 . 5 ) 2 = 2 . 5 2 2 = 2 . 5