Q. 124.2( 5 Votes )

# In an isosceles triangle ABC, if AB = AC = 13 cm and the altitude from A on BC is 5 cm, find BC.

Answer :

**Given: **isosceles triangle ABC, where AB = AC = 13 cm and the altitude from A on BC is 5 cm.**To find: **The value of BC.**Solution:**

In ADB

AD^{2}+BD^{2}=AB^{2}

5^{2}+BD^{2}=13^{2}

25+BD^{2}=169

BD^{2}=169-25

BD^{2}=144

BD=

BD=12cm

In ADB and ADC

∠ADB=∠ADC =90

AB=AC=13cm

AD=AD (Common)

ADB≅ADC (By RHS condition)

BD=CD=12cm (c.p.c.t)

As BC=BD+DC

BC=12+12

BC = 24cm

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