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In a △ABC, AD is the altitude from A such that AD = 12 cm. BD = 9 cm and DC = 16 cm. Examine if △ABC is right angled at A.

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Best answer

Consider △ADC,

∠ADC = 90o (AD is an altitude on BC)

Using the Pythagoras theorem, we get

12+ 16= AC2

AC2 = 144 + 256

= 400

AC = 20 cm

Again consider △ADB,

∠ADB = 90o (AD is an altitude on BC)

Using the Pythagoras theorem, we get

12+ 9= AB2

AB= 144 + 81 = 225

AB = 15 cm

Consider △ABC,

BC2 = 252 = 625

AB2 + AC2 = 152 + 20= 625

AB2 + AC2 = BC2

Because it satisfies the Pythagoras theorem, therefore △ABC is right angled at A.

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