Multiple choice

If the hypotenuse of a right angled triangle is 15 cm and one side of it 6cm less than the hypotenuse, the other side b is equal to.

  1. 12 cm

  2. 21 cm

  3. 9 cm

  4. Ambigous
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A Correct answer
Explanation

Let the hypotenuse c = 15. One side a = 15 - 6 = 9. Using the Pythagorean theorem, a^2 + b^2 = c^2, so 9^2 + b^2 = 15^2. This gives 81 + b^2 = 225, so b^2 = 144, and b = 12.

AI explanation

The given side is 6 cm less than the hypotenuse of 15 cm, making it 9 cm. Using the Pythagorean theorem, the other side squared equals the hypotenuse squared minus the given side squared: 15 squared minus 9 squared equals 225 minus 81, which is 144. The square root of 144 is 12 cm.

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