Here the two sides AB and AC are equal, so we can conclude that

the\({\triangle} ABC\) is isosceles.

Now the minimum length from A to BC will be the perpendicular line.

Since the \({\triangle} ABC\) is isosceles and perpendicular line from A to BC will meet at the midpoint D (as shown in the figure)

Now consider the \({\triangle} ABD\)

AB = 100 , BD =80 and we need to find AD

Using Pythagoras theorem

AD = \(\sqrt{(10000 - 6400)}\) = 60

or we can see that the sides of \({\triangle} ABD\) are in the ratio 3:4:5

= 60:80:100

Ans = 60