Asked by skd
what is the length of side AB in triangle ABC with AB=AC, BC=8, and median CD=9
Answers
Answered by
Reiny
I will assume that D is the midpoint of AB
draw the median from A to BC to meet BC at E
let the intersection of these two medians be F
Since you have an isosceles triangle that median will meet BC at right angles.
Also the medians intersect each other in the ratio of 2:1, the longer side towards the vertex.
Then FC = 6
by Pythagoras
FE^2 + 16 = 36
FE = √20
then AE = 3√20
finally AC^2 = AE^2 + EC^2
= 180 + 16
= 196
AC = √196 = 14
But AB = AC
so AB = 14
draw the median from A to BC to meet BC at E
let the intersection of these two medians be F
Since you have an isosceles triangle that median will meet BC at right angles.
Also the medians intersect each other in the ratio of 2:1, the longer side towards the vertex.
Then FC = 6
by Pythagoras
FE^2 + 16 = 36
FE = √20
then AE = 3√20
finally AC^2 = AE^2 + EC^2
= 180 + 16
= 196
AC = √196 = 14
But AB = AC
so AB = 14
There are no AI answers yet. The ability to request AI answers is coming soon!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.