67 252
Assignments Done
99,3%
Successfully Done
In November 2018

Answer to Question #230 in Geometry for Todd

Question #230
The radius of the inscribed circle of the triangle equals 1, heights are integers. Prove that the triangle is equilateral.
Expert's answer
In any triangle height is bigger than the diameter of inscribed circle. Thus heights of given triangle are integers bigger than 2, that's why all of them are not less than 3. Let S be the square of the triangle, a – its biggest side, h – corresponding height. Suppose that the triangle is not equatorial. Then its perimeter P is less than 3a. Thus 3a > P = Pr = 2S = ha, i.e. h < 3 – a contradiction.

Need a fast expert's response?

Submit order

and get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!

Comments

No comments. Be first!

Leave a comment

Ask Your question

Submit
Privacy policy Terms and Conditions