Question:** A triangle has sides of lengths 7 cm, 24 cm, and 25 cm. Is this triangle a right triangle?
["Is a Triangle with Sides 7 cm, 24 cm, and 25 cm a Right Triangle? A Simple Proof Explained", "When studying geometry, one of the most fundamental questions you may encounter is whether a triangle is a right triangle. The classic example often tested is a triangle with side lengths 7 cm, 24 cm, and 25 cm: Is this a right triangle? The good news is — yes, it is! Let’s explore how to determine this using the Pythagorean Theorem.", "### Understanding the Pythagorean Theorem", "The Pythagorean Theorem states that in a right triangle, the square of the longest side (called the hypotenuse) is equal to the sum of the squares of the other two sides:\n[\na^2 + b^2 = c^2\n]\nwhere ( c ) is the hypotenuse, and ( a ) and ( b ) are the other two sides.", "### Identifying the Longest Side", "Given the side lengths:\n- 7 cm\n- 24 cm\n- 25 cm", "The longest side is 25 cm, which we assume to be the hypotenuse.", "### Applying the Pythagorean Theorem", "Let’s test the sides:\n[\n7^2 + 24^2 = ?\n]\nCompute the squares:\n[\n49 + 576 = 625\n]\nNow calculate the square of the hypotenuse:\n[\n25^2 = 625\n]", "Since\n[\n7^2 + 24^2 = 25^2 \quad \ ext{(625 = 625)}\n]\nthe triangle satisfies the Pythagorean Theorem.", "### Conclusion", "This confirms that a triangle with sides 7 cm, 24 cm, and 25 cm is indeed a right triangle, with the 25 cm side being the right angle’s opposite side.", "### Why This Matters", "Understanding whether a triangle is right-angled is essential in fields like architecture, engineering, and computer graphics then. Museum visitors at science centers often explore interactive triangles to build intuition about geometric principles — and verifying known examples like this triangle helps reinforce learning.", "Key Takeaway:\nThe triangle with sides 7 cm, 24 cm, and 25 cm is a perfect right triangle, demonstrating how classical geometric knowledge applies cleanly to specific cases.", "---", "Try checking triangles like this during your next study session — and remember: square your sides, test the equation, and let the theorem guide your discovery!"]
