A triangle has sides of length 7 cm, 24 cm, and 25 cm. Determine if this triangle is a right triangle.

["Is a Triangle With Sides 7 cm, 24 cm, and 25 cm a Right Triangle?", "When studying triangles, one essential question frequently arises: Is this triangle a right triangle? A triangle is classified as a right triangle if the square of the longest side (the hypotenuse) equals the sum of the squares of the other two sides. For the triangle with sides 7 cm, 24 cm, and 25 cm, we can quickly determine its type using the Pythagorean Theorem.", "### Understanding the Pythagorean Theorem", "The Pythagorean Theorem states that in a right triangle,\n[\na^2 + b^2 = c^2\n]\nwhere ( c ) is the length of the hypotenuse (the longest side), and ( a ) and ( b ) are the lengths of the other two sides.", "### Applying the Values", "Given sides:\n- 7 cm\n- 24 cm\n- 25 cm", "Here, 25 cm is the longest side, so we assume it is the hypotenuse. We apply the theorem:", "Calculate the squares:\n- ( 7^2 = 49 )\n- ( 24^2 = 576 )\n- ( 25^2 = 625 )", "Now, check the relationship:\n[\n7^2 + 24^2 = 49 + 576 = 625\n]\n[\n25^2 = 625\n]", "Since ( 7^2 + 24^2 = 25^2 ), the triangle satisfies the Pythagorean condition.", "### Conclusion", "Yes, a triangle with side lengths 7 cm, 24 cm, and 25 cm is a right triangle. The longest side (25 cm) squared exactly matches the sum of the squares of the other two sides, confirming it as a right triangle. This type of triangle features one 90-degree angle, making it a fundamental example in geometry.", "### Why This Matters", "Identifying right triangles is essential in mathematics, architecture, engineering, and navigation. Knowing whether a triangle is right-angled helps solve problems involving distances, slopes, and stability.", "If you’re examining a triangle and want to avoid guesswork:\n- Identify the longest side.\n- Compute the squares of all three sides.\n- Check if the sum of the two smaller squares equals the largest square.", "This simple method saves time and boosts confidence in geometric assessments.", "Key Takeaway:\nBecause ( 7^2 + 24^2 = 25^2 ), the triangle with sides 7 cm, 24 cm, and 25 cm is definitively a right triangle."]