In a triangle ABC, AB = 13, BC = 14 and AC = 15 cm. AD is the perpendicular drawn from A to BC. Find the length of AD.
Explanation:
We can draw the following diagram from the information given below.
In △ABD: AB2 = BD2 + AD2 ⇒ AD2 = 169 - x2 ...(1)
In △ACD: AC2 = CD2 + AD2 ⇒ AD2 = 225 - (14 - x)2 ...(2)
(1) = (2) ⇒ 169 - x2 = 225 - (14 - x)2 ⇒ 28x = 140 ⇒ x = 5
⇒ AD2 = 169 - 25 = 144 [from (1)] ⇒ AD = 12
Hence, option (d).
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