Mathematics
In the figure given below, AD ⊥ BC, AB = 25 cm, AC = 17 cm and AD = 15 cm. Find the length of BC.
Pythagoras Theorem
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Answer
By pythagoras theorem,
In right angle triangle ADB,
⇒ AB2 = AD2 + BD2
⇒ 252 = 152 + BD2
⇒ 625 = 225 + BD2
⇒ BD2 = 625 - 225 = 400
⇒ BD = = 20 cm
In right angle triangle ADC,
⇒ AC2 = AD2 + DC2
⇒ 172 = 152 + DC2
⇒ 289 = 225 + DC2
⇒ DC2 = 289 - 225 = 64
⇒ DC = = 8 cm
From figure,
⇒ BC = BD + DC = 20 + 8 = 28 cm.
Hence, BC = 28 cm.
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