what is the length of side AB in triangle ABC with AB=AC, BC=8, and median CD=9
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
To find the length of side AB in triangle ABC, we can use the property of medians in a triangle. The length of a median is equal to half the length of the side it bisects.
In this case, we are given that median CD has a length of 9. Since median CD bisects side AB, we can say that AB is twice the length of CD.
Therefore, AB = 2 * CD = 2 * 9 = 18.
Hence, the length of side AB is 18 units.