Multiple choice

Directions: Select the correct alternative from the given choices. Find the radius (in cm) of the circle inscribed inside a triangle with sides measuring 40 cm, 42 cm and 58 cm respectively.

  1. 10

  2. 12

  3. 14

  4. 16
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The sides are 40, 42, 58. This is a right triangle because 40^2 + 42^2 = 1600 + 1764 = 3364 = 58^2. The inradius r = (a + b - c) / 2 = (40 + 42 - 58) / 2 = 24 / 2 = 12.

AI explanation

We first verify the triangle is right-angled by checking that 40 squared plus 42 squared equals 58 squared, since 1600 plus 1764 equals 3364. The area of this right triangle is half the product of the perpendicular sides, giving an area of 840 square centimeters. Using the inradius formula r equals Area divided by semi-perimeter, the semi-perimeter is 70 centimeters. The inradius is 840 divided by 70, which equals 12 centimeters.

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