That altitude is large
Geometry
Level
3
Two of the altitudes of a scalene triangle have lengths 4 and 12. if the length of the remaining altitude is also an integer, then what is its maximum value?
The answer is 5.
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1 solution
Altitude length drawn from a vexter of a triangle is given by
2(area of triangle)/(length of side opposite to the vertex).
So , as two altitude lengths are given as 4,12.
Let us assume area of triangle = S,
a,b,c be lengths of sides of triangle.
So , 4 = 2S/a , 12 = 2S/b,
Now we have to find the value of 2S/c = x,
So , a+b > c,
So , we get x > 3,
And b+c > a,
So x < 6,
Given triangle is scalene and altitude length is integer , so x = 5 .