Multiple choice

What is the area of a right-angled triangle, if the radius of the circumcircle is 5 cm and altitude drawn to the hypotenuse is 4 cm?

  1. 20 cm2

  2. 18 cm2

  3. 16 cm2

  4. 10 cm2
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A Correct answer
Explanation

In a right-angled triangle, the circumradius R is half the hypotenuse (h). Thus, h = 2 * 5 = 10 cm. The area is (1/2) * base * height = (1/2) * hypotenuse * altitude_to_hypotenuse = (1/2) * 10 * 4 = 20 cm^2.

AI explanation

In a right-angled triangle, the hypotenuse acts as the diameter of the circumcircle, making the hypotenuse 10 cm. The area of a triangle is half the product of its base and height, so using the hypotenuse as the base and the given altitude gives 0.5 multiplied by 10 multiplied by 4. This calculates to 20 square cm.

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