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Question : In $\triangle$ABC, $\angle$BAC = 90º and AD is perpendicular to BC. If AD = 6 cm and BD = 4 cm, then the length of BC is:

Option 1: 10 cm

Option 2: 12 cm

Option 3: 13 cm

Option 4: 15 cm


Team Careers360 3rd Jan, 2024
Answer (1)
Team Careers360 15th Jan, 2024

Correct Answer: 13 cm


Solution :

As we know the altitude to the hypotenuse divides the triangle into two triangles that are similar to the original triangle and each other.
⇒ AD 2 = BD × DC
⇒ 6 2 = 4 × DC
⇒ DC = 9 cm
⇒ BC = BD + DC
⇒ BC = 4 + 9 =13 cm
Hence, the correct answer is 13 cm.

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