If the length of the sides of a triangle are in the ratio 5 : 12 : 13, find the ratio of the length of the altitudes of the respective sides.
Explanation:
Let the three sides are 5a, 12a and 13a.
Area of triangle = 12 × side1 × height1 = 12 × side2 × height2 = 12 × side3 × height3
Hence, 5a × altitude1 = 12a × altitude2 = 13a × altitude3.
altitude1 : altitude2 : altitude3 = 15:112:113 = 156 ∶ 65 ∶ 60
Hence, option (c).
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