Question

Base ‘BC’ of an isosceles ∆ABC is 20 cm and equal sides is 26 cm, then the length of altitude through the vertex ‘A’ is

(A)23 cm (B)24 cm (C)25 cm (D)26 cm

Answer 1

Draw perpendicular AD In isosceles triangle ABC ,BD =CD=10 cm In right angled triangle ABD use Pythagoras theorem ,h²=p² +b², therefore AD(p)=√676-100=√576=24

Answer 2

Draw a perpendicular from A on to BC.  It will meet BC at the center D of BC.  This can be show n  from the symmetry.

Apply Pythagoras formula in  triangle  ADB or ADC,
         26² = AD² + (BC/2)² =  AD² + 10²

           AD = 24 cm