A triangle has sides of length 7, 24, and 25. Determine if it is a right triangle.
["# Is a Triangle with Sides 7, 24, and 25 a Right Triangle?", "When exploring triangles, one essential question often arises: Is this triangle a right triangle? A key characteristic of right triangles is defined by the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the longest side) equals the sum of the squares of the other two sides.", "This article examines whether a triangle with side lengths 7, 24, and 25 is indeed a right triangle by applying the Pythagorean theorem.", "## Understanding the Pythagorean Theorem", "The Pythagorean theorem confirms that for any right triangle with legs (a) and (b), and hypotenuse (c) (where (c) is the longest side), the following equation holds:", "[\na^2 + b^2 = c^2\n]", "If this equality is true, the triangle is right-angled; otherwise, it is not.", "## Apply the Theorem to the Given Triangle", "The given side lengths are 7, 24, and 25. First, identify the longest side to determine the potential hypotenuse:", "- (c = 25) (longest side)\n- (a = 7), (b = 24)", "Now calculate both sides of the equation:", "### Left side: Sum of the squares of the two shorter sides\n[\na^2 + b^2 = 7^2 + 24^2 = 49 + 576 = 625\n]", "### Right side: Square of the longest side\n[\nc^2 = 25^2 = 625\n]", "## Analyze the Result", "Since\n[\na^2 + b^2 = 625 = 25^2 = c^2\n]\nthe Pythagorean theorem is satisfied.", "## Conclusion", "Yes, a triangle with sides of lengths 7, 24, and 25 is a right triangle. The side of length 25 is the hypotenuse, and the other two sides are the legs that satisfy the Pythagorean relation. This triangle exemplifies a classic Pythagorean triple, used frequently in geometry and real-world applications involving right angles.", "Understanding whether a triangle is right-angled helps in solving problems in physics, architecture, and engineering—fields that rely heavily on accurate geometric principles.", "---", "Keywords: right triangle, triangle sides 7 24 25, Pythagorean theorem, right triangle verification, geometry, right triangle identification, 7-24-25 triangle, apply Pythagorean theorem", "Meta Description: Verify if a triangle with side lengths 7, 24, and 25 is a right triangle using the Pythagorean theorem. Learn how to determine right angles using the sum of squares of sides."]
