A triangle has side lengths of 7, 24, and 25 units. Determine if it is a right triangle.
["# Is Triangle with Side Lengths 7, 24, and 25 a Right Triangle?", "When it comes to geometry, one of the most fundamental questions is whether a triangle is a right triangle—a triangle where one angle measures exactly 90 degrees. A quick and reliable way to identify a right triangle is by applying the Pythagorean Theorem. In this article, we’ll explore whether a triangle with side lengths of 7, 24, and 25 units qualifies as a right triangle.", "## Understanding the Pythagorean Theorem", "The Pythagorean Theorem states that in any right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. Mathematically, it’s expressed as:", "[\na^2 + b^2 = c^2\n]", "where ( c ) is the hypotenuse and ( a ), ( b ) are the other two sides.", "## Assigning Side Lengths", "Given triangle sides of 7, 24, and 25 units, we must first identify which side, if any, could be the hypotenuse. Since 25 is the largest side, it must be checked whether:", "[\n7^2 + 24^2 = 25^2\n]", "Let’s calculate each value.", "- ( 7^2 = 49 )\n- ( 24^2 = 576 )\n- ( 25^2 = 625 )", "Now add the squares of the two shorter sides:", "[\n7^2 + 24^2 = 49 + 576 = 625\n]", "Compare this sum to the square of the largest side:", "[\n625 = 625\n]", "## Conclusion: This Is a Right Triangle", "Since the equation ( 7^2 + 24^2 = 25^2 ) holds true, the triangle with side lengths 7, 24, and 25 is indeed a right triangle. The side of length 25 is the hypotenuse, and the angles opposite the sides of 7 and 24 are acute angles forming a perfect 90-degree right angle.", "This verification confirms the triangle’s classification through a classic mathematical principle. Whether for academic study, practical measurement, or visual design, identifying right triangles using the Pythagorean Theorem is essential and straightforward.", "### Bonus: Real-World Application", "Triangles like this are not just theoretical. Right triangles with sides 7, 24, 25 appear in construction, navigation, and engineering, where right angles and accurate measurements are critical.", "---", "Keywords for SEO: right triangle 7 24 25, Pythagorean Theorem check, right triangle verification, 7-24-25 triangle, geometry proof, hypotenuse triangle, mathematical verification, right triangle examples", "Meta Description: Verify if a triangle with sides 7, 24, and 25 units is a right triangle using the Pythagorean Theorem. Trova mathematical proof, right triangle classification, and practical applications."]
