Multiple choice

If the length of the hypotenuse of a right-angled isosceles triangle is 12 cm, then the area of that triangle (in sq. cm) is

  1. 72

  2. 36

  3. 144

  4. 24
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B Correct answer
Explanation

In a right-angled isosceles triangle with hypotenuse h, the legs are equal (say x). By Pythagoras, x^2 + x^2 = h^2, so 2x^2 = 12^2 = 144, meaning x^2 = 72. The area is (1/2) * base * height = (1/2) * x * x = (1/2) * 72 = 36.

AI explanation

In a right-angled isosceles triangle, the perpendicular legs are of equal length, so by the Pythagorean theorem, the hypotenuse squared equals the sum of the squares of the two equal sides, expressed as h squared equals 2 times a squared. With the hypotenuse given as 12 cm, we have 12 squared equals 2 times a squared, so 144 equals 2 times a squared, making a squared equal to 72. The area of the triangle is half the product of the base and height, calculated as 1 divided by 2 multiplied by a squared, which gives 36 square centimeters. The area is 36.

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