Multiple choice

The legs of a right angled triangle are 8 cm and 15 cm. The radius of the circle inscribed in the triangle (in cm), is _________.

  1. 1

  2. 2

  3. 3

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

For a right triangle with legs a and b and hypotenuse c, the inradius r = (a + b - c) / 2. Here, a = 8, b = 15, so c = sqrt(8^2 + 15^2) = 17. r = (8 + 15 - 17) / 2 = 6 / 2 = 3.

AI explanation

The radius of an incircle is given by the formula r equals the area of the triangle divided by the semi-perimeter. For legs of 8 cm and 15 cm, the hypotenuse is the square root of 8 squared plus 15 squared, which equals 17 cm, making the perimeter 8 plus 15 plus 17 equals 40 cm and the semi-perimeter 20 cm. The area is one half times 8 times 15, which equals 60 square cm, so the radius is 60 divided by 20, resulting in 3 cm.

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