Multiple choice

What is the radius of the circle inscribed in a triangle whose sides are 4 cm, 7.5 cm and 8.5 cm?

  1. 1.5 cm

  2. 2 cm

  3. 2.5 cm

  4. 3 cm
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The sides are 4, 7.5, and 8.5. Since 4^2 + 7.5^2 = 16 + 56.25 = 72.25 = 8.5^2, it is a right-angled triangle. The inradius r of a right triangle is (a+b-c)/2 = (4 + 7.5 - 8.5)/2 = 3/2 = 1.5 cm.

AI explanation

Using the property of a right triangle, the squares of the two smaller sides sum to the square of the largest side (4^2 + 7.5^2 = 8.5^2), so the semi-perimeter is (4 + 7.5 + 8.5) / 2 = 10 cm. The area of the triangle is 1/2 * 4 * 7.5 = 15 sq cm. The radius of the inscribed circle is Area / semi-perimeter, which is 15 / 10 = 1.5 cm. The result is 1.5 cm.

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