Multiple choice

If the two legs of a right angled triangle are equal and the square of the hypotenuse is $100cm^2$, then the length of each leg is _________.

  1. $10$cm
  2. $5\sqrt{2}$cm
  3. $10\sqrt{2}$cm
  4. $13\sqrt{2}$cm
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let the legs be x. By Pythagorean theorem, x^2 + x^2 = hypotenuse^2. 2x^2 = 100. x^2 = 50. x = sqrt(50) = 5 * sqrt(2).

AI explanation

Let the equal legs be x; using the Pythagorean theorem, the sum of their squares equals the square of the hypotenuse, so x squared plus x squared equals 100. This simplifies to 2 times x squared equals 100, meaning x squared is 50. Taking the square root gives x equal to the square root of 50, which simplifies to 5 root 2 cm.

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