A triangle has sides of lengths 7, 24, and 25 meters. Determine if it is a right triangle.
["Is a Triangle with Side Lengths 7, 24, and 25 Meters a Right Triangle?", "When exploring geometric shapes, one key question often arises: Is a triangle a right triangle? This is especially relevant when given the lengths of all three sides. In this article, we’ll examine whether a triangle with sides measuring 7 meters, 24 meters, and 25 meters forms a right triangle and explain 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 (the hypotenuse) is equal to the sum of the squares of the other two shorter sides. For a triangle with sides ( a ), ( b ), and ( c ), where ( c ) is the longest side, the triangle is a right triangle if:", "[\na^2 + b^2 = c^2\n]", "This test works because the equality confirms the right angle between the two legs forming the hypotenuse.", "### Applying the Theorem to the Triangle with Sides 7, 24, and 25", "Given the side lengths:\n- ( a = 7 ) meters\n- ( b = 24 ) meters\n- ( c = 25 ) meters (longest side)", "We calculate:", "[\na^2 + b^2 = 7^2 + 24^2 = 49 + 576 = 625\n]", "[\nc^2 = 25^2 = 625\n]", "Since ( a^2 + b^2 = c^2 ) (625 = 625), the condition holds true.", "### Is This a Right Triangle?", "Yes, the triangle with sides 7 m, 24 m, and 25 m is indeed a right triangle. This well-known set of side lengths is an example of a Pythagorean triple—specifically, (7, 24, 25). This means it has a right angle between the sides of length 7 meters and 24 meters, with 25 meters as the hypotenuse.", "### Practical Implications", "Recognizing a right triangle provides valuable geometric and real-world insights. Right triangles are fundamental in construction, navigation, and engineering because they guarantee a perfect 90-degree angle, enabling accurate measurements and stable structures.", "### Conclusion", "Using the Pythagorean Theorem, we confirm that a triangle with sides 7, 24, and 25 meters satisfies the condition for being a right triangle. This combination forms a classic right-angled triangle, proving both mathematically and visually. Whether for academic study, practical application, or curiosity, verifying right triangles using side lengths and theory is essential in geometry and beyond.", "---", "Keywords: right triangle, Pythagorean theorem, 7-24-25 triangle, geometry, right angle, triangle verification, 7 meters side, 24 meters side, 25 meters triangle"]
