Question

Ratio of sides of traignle are given find ratio of altitudes drawn to them

Answer 1

Let the sides of the triangle be a, b, and c. The altitudes are given in the ratio of 1:2:3. So we can let x be such that the altitudes have lengths x,2x, and 3x. Let x be the length of the altitude drawn to side a. Let 2x be the length of the altitude drawn to side b. Let 3x be the length of the altitude drawn to side c. Now we use the usual formula for the area of a triangle, which is Area of a triangle = ·(any side of triangle)·(altitude drawn to that side) Therefore Area of the triangle = a·x = b·2x = ·3x a·x = b·2x = c·3x Multiply by 2 a·x = 2b·x = c·3x ax = 2bx = 3cx Divide by x a = 2b = 3c We are given that the perimeter is 36, so P = a + b + c = 36 So we have the system a = 2b a = 3c a + b + c = 36