Q. 45

# 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 :

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,

⇒ AB^{2} = BD^{2} + AD^{2}

⇒ 25^{2} = 7^{2} + AD^{2}

⇒ AD^{2} = 625 – 49 = 576

⇒ AD = 24

∴ Measure of altitude from A to BC is 24 cm

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