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प्रश्न
In an isosceles triangle ABC, if AB = AC = 13 cm and the altitude from A on BC is 5 cm, find BC.
उत्तर
In ΔADB, by Pythagoras theorem
AD2 + BD2 = 132
⇒ 25 + BD2 = 169
⇒ BD2 = 169 − 2 = 144
⇒ BD = `sqrt144` = 12 cm
In ΔADB and ΔADC
∠ADB = ∠ADC [Each 90°]
AB = AC [Each 13 cm]
AD = AD [Common]
Then, ΔADB ≅ ΔADC [By RHS condition]
∴ BD = CD = 12 cm [By c.p.c.t]
Hence, BC = 12 + 12 = 24 cm
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