Tri... Angle...
The lengths of the sides of triangle ABC are consecutive positive integers. D is the midpoint of BC, and AD is perpendicular to the bisector of angle C.
What is the length of the shortest side divided by the length of the largest side multiplied by the length of the remaining side?
Express your answer as a decimal
The answer is 1.5.
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1 solution
Let the triangle sides be AC = n, AB = (n+1) & BC= (n+2). Now since the angle bisector of C is perpendicular to AD, we can say that ACcos(C/2)=CDcos(C/2). In other words, n = (n+2)/2 or n=2. This implies that the sides of the triangle are 2, 3 & 4 which, in turn, means the required fraction = 2*3/4 = 1.5