SOLUTION: C.is the right angle in triangle ABC.D is the midpoint of side AC.E is the midpoint of side BC. The lenght of line segment BD is 26 The lenght of line segment AE is 7 How long

Algebra ->  Triangles -> SOLUTION: C.is the right angle in triangle ABC.D is the midpoint of side AC.E is the midpoint of side BC. The lenght of line segment BD is 26 The lenght of line segment AE is 7 How long       Log On


   

Question 323713: C.is the right angle in triangle ABC.D is the midpoint of side AC.E is the midpoint of side BC.
The lenght of line segment BD is 26
The lenght of line segment AE is 7
How long is the side AB?
thankyou
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
AC%5E2%2BBC%5E2=AB%5E2
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.
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AC%5E2%2BCE%5E2=AE%5E2=49
AC%5E2%2B%28BC%2F2%29%5E2=49
1.AC%5E2%2BBC%5E2%2F4=49
.
.
.
BC%5E2%2BCD%5E2=26%5E2
BC%5E2%2B%28AC%2F2%29%5E2=676
2.BC%5E2%2BAC%5E2%2F4=676
.
.
Add eq. 1 and eq. 2,
AC%5E2%2BBC%5E2%2F4%2BBC%5E2%2BAC%5E2%2F4=49%2B676
%285%2F4%29AC%5E2%2B%285%2F4%29BC%5E2=725
AC%5E2%2BBC%5E2=%284%2F5%29%28725%29
AB%5E2=580
AB=sqrt%28580%29
AB=2sqrt%28145%29