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AD is the altitude from A to BC in triangle ABC, where AB = 13 cm, AC = 20 cm and BC = 21 cm. Find AD.

Competition practiceGeometry

A12 cm
B16 cm
C10 cm
D9 cm

Step-by-Step Solution

Let BD =

x

. Then

1 3^{2} - x^{2} = 2 0^{2} - (21 - x)^{2}

, i.e.

169 = - 41 + 42 x

, so

x = 5

. Hence

A D = 169 - 25 = 12

cm.

Answer: A) 12 cm

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