Question

if an isosceles triangle ABC if AB =AC =25 cm and BC=45 CM, then the measure of altitude from A on BC is

Answer 1

Let AD be the altitude where D is a point on BC.

In triangle ADB,

AD=?

AB=25cm

DB = 1/2*BC ( because altitude of an isoceles triangle divides it into two congruent triangles =>ADB and ADC are congruent and DB=DC)

DB=1/2*14=7cm

In right angled triangle ABD,

( ryt angled as altitude is perpendicular)

(AB)^2=(AD)^2+(BD)^2 [pythagoras theorem]

=> (25)^2=(AD)^2+(7)^2

=>625=(AD)^2+49

=>625-49=(AD)^2

=>576=(AD)^2

=>(24)^2=(AD)^2

Squares will be cancelled

=>AD=24 cm