Question

ABC is an isosceles triangle with AB = AC = 13 cm and BC = 10 cm. Calculate the length (in cm) of the perpendicular from A to BC.

Answer 1

Let the perpendicular from A cuts BC at D. In an Isosceles triangle the perpendicular on non congruent side bisects the non congruent side.
Hence, In $△ABD$,
$A{B}^2=B{D}^2+A{D}^2$ (Pythagoras theorem)
${13}^2=5^2+A{D}^2$
$A{D}^2=144$
$AD=12$ cm