A triangle has sides of 7, 24, and 25 units. Is it a right triangle?

["Is a Triangle with Sides 7, 24, and 25 Units a Right Triangle?", "When exploring triangles in geometry, one fundamental question often arises: Is this triangle a right triangle? A key way to determine this is by using the Pythagorean Theorem, which 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 sides.", "Let’s analyze the triangle with side lengths 7, 24, and 25 units.", "### Step 1: Identify the longest side\nThe longest side is 25 units, which would be the hypotenuse if this is a right triangle.", "### Step 2: Apply the Pythagorean Theorem\nCheck if:\n[\n7^2 + 24^2 = 25^2\n]", "Calculate each square:\n- (7^2 = 49)\n- (24^2 = 576)\n- (25^2 = 625)", "Now, add the squares of the two shorter sides:\n[\n49 + 576 = 625\n]", "Since (625 = 625), the equation holds true.", "### Conclusion\nThe triangle with sides 7, 24, and 25 is indeed a right triangle, where 25 is the hypotenuse. This means it satisfies all conditions of right-angled geometry, such as the Pythagorean relationship, and angles opposite these sides confirm a 90-degree angle between the sides of 7 and 24.", "Whether you're solving math problems, studying geometry, or exploring mathematical proofs, recognizing right triangles through the Pythagorean Theorem is essential—and this triangle is a classic example that shows how simple numbers can form classic right triangles.", "Key takeaway:\n✔ A triangle with sides 7, 24, and 25 is a right triangle.\n✔ Confirmed via: (7^2 + 24^2 = 25^2) (i.e., (49 + 576 = 625)).\n✔ This makes it a perfect illustration of a Pythagorean triple."]