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Question

Ratio of sides of triangle ABC is 1 : 2 : 4 , ratio of altitude drawn into these sides is ?
 


Solution

As you know in any triangle, the area of triangle is given by 12 bh, where b is the side and h is altitude from opposite vertex to the side.
Hence, product of bh is always constant for a given triangle.
This means if the sides are in the ratio of 1:2 : 4, the altitudes must have a ratio which is reciprocal of this ratio.
Hence, the altitudes are in ratio fo 4: 2 :1.
Check:
Let the sides be 1 unit, 2 unit and 4 units and corresponding altitudes are 4 units, 2 units and 1 unit respectively.
Then the area of triangle =12×1×4=2 sq units
12×2×2=2 sq units
12×4×1=2sq.units

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