Question

In an isoceles triangle abc, ab=ac=13cm and the altitude from a on bc is 5 cm find bc?

Answer 1

As altitude is perpendicular bisector it will form a right angle at the base bc..
in right angle triangle abc
measure of angle fromed by altitude is 90 degrees
therefore, by pythagorus theorem
square of 13 = square of 5 (altitude) + square of the half of the base bc
therefore, 169 = 25 + square of the half of the base bc
169 - 25 = square of the half of the base bc
144 = square of the half of the base bc
12 = half of the base bc...... <---- (here you are taking square roots on both sides)
therefore, 24 = base bc 
Thanks!