Geometry Practice : Inradius

This aptitude practice question is a geometry question. Concept tested: Computing inradius of a triangle if the sides of the triangle are known.

Question

What is the measure of in radius of the triangle whose sides are 24, 7 and 25?

1. 12.5
2. 3
3. 6
4. None of these

  Correct Answer      Choice (2). The inradius of the triangle measures 3 units.

Explanatory Answer

We know that for any triangle, area of the triangle = r * s, where r is the in radius and s is the semi perimeter

24, 7, 25 is a Pythagorean triplet. ∴ the given triangle is a right angled triangle
As the given triangle is a right angled triangle, area of the triangle = \\frac{1}{2})* 24 * 7 = 84 sq units.
Semi perimeter, s = \\frac{a + b + c}{2}) = \\frac{24 + 7 + 25}{2}) = 28
Therefore, 84 = 28 * r
=> r = \\frac{84}{28}) = 3

Alternative Method

If the given triangle is a right triangle, its in radius can be computed using the formula r = s - h, where 'r' is the in radius, 's' is the semi perimeter and 'h' is the hypotenuse
In this triangle, semiperimeter, s = 28 and hypotenuse, h = 25
∴ r = 28 - 25 = 3 units.

  The correct answer is Choice (2).