Question

In an isosceles triangle ABC, if AB = AC = 25 cm and BC = 14 cm, then the measure of altitude from A on BC is 

A. 20 cm 

B. 22 cm 

C. 18 cm 

D. 24 cm

Answer 1

Given in an isosceles ΔABC, AB = AC = 25 cm and BC = 14 cm 

Here altitude from A to BC is AD. 

We know in isosceles triangle altitude on non-equal sides is also median. 

⇒ BD = CD = BC/2 = 7 cm 

Applying Pythagoras Theorem, 

⇒ AB² = BD² + AD² 

⇒ 25² = 7² + AD² 

⇒ AD² = 625 – 49 = 576 

⇒ AD = 24 

∴ Measure of altitude from A to BC is 24 cm