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
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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