Multiple choice

The area of a right angled triangle is $30cm^2$ and the length of its hypotenuse is $13 cm$. The length of the shorter side is $5 cm$.

  1. True

  2. False
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A Correct answer
Explanation

For a right triangle with hypotenuse 13, the sides must satisfy a^2 + b^2 = 13^2 = 169. If one side is 5, the other is sqrt(169 - 25) = 12. The area is (1/2) * 5 * 12 = 30. The statement is true.

AI explanation

If the hypotenuse is 13 cm and the shorter leg is 5 cm, the third side is found by the Pythagorean theorem: sqrt(13^2 - 5^2) = 12 cm. The area of this triangle is 0.5 times 5 times 12 = 30 cm^2. This matches the stated area exactly, making the statement true.

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