Check if right triangle: \( 7^2 + 24^2 = 49 + 576 = 625 = 25^2 \) â yes.
["Check If It’s a Right Triangle: A Simple Guide Using the Pythagorean Theorem", "Determining whether a triangle is a right triangle can be quick and accurate using the Pythagorean Theorem. This classic mathematical principle states: In a right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides. Mathematically, this is expressed as:", "[\na^2 + b^2 = c^2\n]", "where ( c ) is the hypotenuse and ( a ) and ( b ) are the other two sides.", "### The Classic Example: ( 7^2 + 24^2 = 49 + 576 = 625 ), and ( 25^2 = 625 )", "Let’s apply this to the well-known right triangle with sides 7, 24, and 25:", "- Calculate the squares of the two shorter sides:\n ( 7^2 = 49 )\n ( 24^2 = 576 )", "- Add them together:\n ( 49 + 576 = 625 )", "- The square of the longest side:\n ( 25^2 = 625 )", "Since\n[\n7^2 + 24^2 = 25^2\n]\n✅ Yes, this confirms the triangle with sides 7, 24, and 25 is indeed a right triangle.", "### Why This Works (The Pythagorean Theorem)", "Named after the ancient Greek mathematician Pythagoras, the theorem works only for right triangles. If you plug the side lengths into the formula, the equality holds true—validating the triangle’s right-angle property.", "### How to Check Any Triangle Quickly", "1. Identify the longest side—this is your candidate hypotenuse.\n2. Square each side and add the squares of the two shorter sides.\n3. Compare the sum of the squares to the square of the longest side.\n4. If the two sides match, the triangle is right-angled.", "### Real-Life Applications", "- Geometry and trigonometry lessons\n- Engineering and architecture design\n- Triangle proofs and advanced math problems\n- GPS coordinates and mapping calculations", "### Conclusion", "Checking if a triangle is right-angled doesn’t require complex tools. By applying the Pythagorean Theorem—particularly using examples like ( 7^2 + 24^2 = 25^2 )—you can instantly verify the triangle’s classification. Remember: For a triangle to be right, ( a^2 + b^2 ) must equal ( c^2 ), where ( c ) is the longest side. This simple principle saves time and clarifies geometric concepts every day.", "---", "Keywords for SEO:\nright triangle check, Pythagorean theorem, verify right triangle, triangle geometry proof, 7^2 + 24^2 = 25^2, triangle properties, math problem solving, geometric verification", "Meta Description:\nCheck if a triangle is a right triangle using the Pythagorean Theorem. Learn how ( 7^2 + 24^2 = 25^2 ) proves it’s a right triangle with step-by-step guidance and real-world examples."]
