A triangle has sides of lengths 7 cm, 24 cm, and 25 cm. Verify if it is a right triangle.
["Is a Triangle with Sides 7 cm, 24 cm, and 25 cm a Right Triangle?", "Understanding the properties of triangles is fundamental in geometry, and one key question often asked is whether a triangle with specific side lengths forms a right triangle. A triangle is classified as a right triangle if it satisfies the Pythagorean Theorem — which states that for a right triangle, the square of the length of the longest side (the hypotenuse) equals the sum of the squares of the other two sides.", "---", "### The Triangle with Sides 7 cm, 24 cm, and 25 cm", "Let’s examine the triangle with side lengths:", "- ( a = 7 ) cm\n- ( b = 24 ) cm\n- ( c = 25 ) cm", "Assuming the longest side ( c = 25 ) cm is the hypotenuse, we apply the Pythagorean Theorem:", "[\na^2 + b^2 = 7^2 + 24^2 = 49 + 576 = 625\n]", "Now calculate the square of the longest side:", "[\nc^2 = 25^2 = 625\n]", "Since\n[\na^2 + b^2 = c^2 \quad (625 = 625),\n]", "the triangle satisfies the Pythagorean Theorem exactly.", "---", "### Conclusion: Is It a Right Triangle?", "Yes, a triangle with sides 7 cm, 24 cm, and 25 cm is a right triangle — specifically, a right-angled triangle with legs of 7 cm and 24 cm, and hypotenuse of 25 cm.", "---", "### Why This Triangle Matters", "This triangle is a classic example used in geometry due to its clean integer side lengths (often called a Pythagorean triple) and practical applications in fields like architecture, engineering, and education. Recognizing whether a triangle is right-angled helps in solving problems involving area calculations, distances, and structural design.", "If you ever need to verify a triangle’s type, always test the sides using ( a^2 + b^2 = c^2 ). In this case, the proof is simple and definitive.", "---", "Key Takeaways:", "- Use ( a^2 + b^2 = c^2 ) to test right triangles.\n- A triangle with sides 7, 24, 25 satisfies the equation — it is a right triangle.\n- Always confirm using exact values for accuracy.", "Verify your triangles confidently — geometry reveals wonders hidden in numbers and shapes!"]
