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ΔABC is right angled at B. BD is an altitude. AD = 9 cm and DC = 16 cm. What is the value of BD (in cm)?
- A6
- B18
- C21
- D12
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Discussion 1
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CCommunity
Let the ∠BCD = y
Now in triangle ABC and in BDC
⇒ cos y = BC/25 = 16/BC
⇒ BC2 = 400
⇒ BC = 20
Now applying Pythagoras theorem in triangle BDC
⇒ BD = √(BC2 - DC2)
⇒ BD = √(202 - 162) = √144 = 12
∴ BD = 12 cm
Now in triangle ABC and in BDC
⇒ cos y = BC/25 = 16/BC
⇒ BC2 = 400
⇒ BC = 20
Now applying Pythagoras theorem in triangle BDC
⇒ BD = √(BC2 - DC2)
⇒ BD = √(202 - 162) = √144 = 12
∴ BD = 12 cm