The Ratio of altitudes of a triangle are 1:2:3. Find the ratio of its side.
Answer:
let the triangle be ABC
so area of triangle ABC = 1/2 AB x a = 1/2 BC x b = 1/2 CA x c
where a,b and c are altitudes
a = 1/6 K, b = 2/6K and c= 3/6K, where K is proportionality constant
therefore 1/2 AB x 1/6K = 1/2 BC x 2/6K = 1/2 CA x 3/6K
AB/12 = BC/6 =CA/4
AB:BC::CA = 12:6:4 = 6:3:2
Answer:
let the triangle be ABC
so area of triangle ABC = 1/2 AB x a = 1/2 BC x b = 1/2 CA x c
where a,b and c are altitudes
a = 1/6 K, b = 2/6K and c= 3/6K, where K is proportionality constant
therefore 1/2 AB x 1/6K = 1/2 BC x 2/6K = 1/2 CA x 3/6K
AB/12 = BC/6 =CA/4
AB:BC::CA = 12:6:4 = 6:3:2
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