Shortest Height
Geometry
Level
3
What is the length of the smallest height of a triangle whose sides are 12 , 16 and 20 ?
The answer is 9.6.
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1 solution
As it is a rectangular triangle (12^2+16^2=20^2) we know two of the heights, 12 and 16.
To calculate the other height, notice that ABC and ADC are similar. We can use Thales' Theorem to figure out BD.
1 6 2 0 = B D 1 2
BD= 9.6
9.6 is less than 12 and than 16, so this is the solution.