Consider △ADC,
∠ADC = 90o (AD is an altitude on BC)
Using the Pythagoras theorem, we get
122 + 162 = 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
122 + 92 = AB2
AB2 = 144 + 81 = 225
AB = 15 cm
Consider △ABC,
BC2 = 252 = 625
AB2 + AC2 = 152 + 202 = 625
AB2 + AC2 = BC2
Because it satisfies the Pythagoras theorem, therefore △ABC is right angled at A.