Multiple choice

The maximum area of a triangle inscribed in a semi-circle having radius $10cm$ is ........... ${cm}^{2}$.

  1. $10$
  2. $50$
  3. $100$
  4. $200$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The triangle with maximum area inscribed in a semicircle has its base as the diameter (20 cm) and height as the radius (10 cm). Area = 1/2 * base * height = 1/2 * 20 * 10 = 100.

AI explanation

A triangle inscribed in a semicircle is a right-angled triangle with the diameter as its hypotenuse. To maximize the area, the perpendicular height from the diameter to the circumference must equal the radius of 10 cm. The base is the diameter, which is 2 * 10 = 20 cm. Applying the area formula (1/2) * base * height gives (1/2) * 20 * 10 = 100 cm^2.

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