In triangle FGH, FG=25 cm, FH=24 cm and GH=7 cm. Determine if triangle FGH is a right-angled triangle.

To determine if triangle FGH is a right-angled triangle, we can use the Pythagorean theorem. This theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

Here, we can consider FG as the hypotenuse because it is the longest side.

Step 1: Square the lengths of the two shorter sides and add them together. FH² = 24² = 576 cm² GH² = 7² = 49 cm² FH² + GH² = 576 cm² + 49 cm² = 625 cm²

Step 2: Square the length of the hypotenuse. FG² = 25² = 625 cm²

Step 3: Compare the results. Since FH² + GH² = FG², triangle FGH is a right-angled triangle according to the Pythagorean theorem.