Multiple choice

If the length of the hypotenuse of a right angled triangle is 10 cm, then what is the maximum area of such a right angled triangle?

  1. 100 cm2

  2. 50 cm2

  3. 25 cm2

  4. 10 cm2
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

For a right triangle with hypotenuse h, the area is (1/2) * a * b. Since a^2 + b^2 = h^2, the area is maximized when a = b = h / sqrt(2). Max area = (1/2) * (h/sqrt(2))^2 = h^2 / 4 = 100 / 4 = 25.

AI explanation

For a right-angled triangle with a fixed hypotenuse of 10 cm, the maximum area occurs when the triangle is isosceles, meaning both legs are equal. Using the Pythagorean theorem, a squared plus b squared equals 10 squared, and with a = b, we get 2 times a squared equals 100, so each leg is sqrt(50) cm. The maximum area is one half times base times height, which is one half times sqrt(50) times sqrt(50), equaling 25 square centimeters. The maximum area is 25 square centimeters.

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