Final Answer:
The three right triangles among the given side lengths are:
A. 3cm, 4cm, 5cm
C. 7cm, 24cm, 25cm
D. 11cm, 13cm, 15cm
Step-by-step explanation:
In a right-angled triangle, the Pythagorean theorem states that the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. This theorem helps identify right triangles among given side lengths.
For instance, taking option A: 3² + 4² = 9 + 16 = 25, which is equal to 5². Since the sum of the squares of the smaller sides is equal to the square of the longest side, this follows the Pythagorean theorem, confirming that it is a right triangle.
Similarly, in option C: 7² + 24² = 49 + 576 = 625, which is equal to 25². Once again, the sum of the squares of the smaller sides equals the square of the longest side, validating it as a right triangle.
Lastly, for option D: 11² + 13² = 121 + 169 = 290, which is equal to 15². As the Pythagorean theorem holds true in this case too, with the sum of squares equalling the square of the longest side, this confirms it as a right triangle.
Therefore, the given options A, C, and D satisfy the conditions of the Pythagorean theorem and represent right-angled triangles among the provided side lengths.