Geometry : Right Triangle Properties

This aptitude practice question is a Geometry problem solving question. Concept tested: Pythagorean Triplets, properties of right triangles and method to compute circumradius of a right triangle.

Question

What is the measure of the circum radius of a triangle whose sides are 9, 40 and 41?

1. 6
2. 4
3. 24.5
4. 20.5

  Correct Answer      Choice (4). 20.5

Explanatory Answer

From the measure of the length of the sides of the triangle, 9, 40 and 41 we can infer that the triangle is a right angled triangled. 9-40-41 is a Pythagorean triplet.
In a right angled triangle, the circum radius is half the hypotenuse.
In the given triangle, the hypotenuse = 41.
Therefore, the circum radius = \\frac{41}{2}) = 20.5 units.

  The correct answer is Choice (4).