A triangle has sides of 7 cm, 24 cm, and 25 cm. Is it a right triangle?
["Is This Triangle a Right Triangle? Understanding the 7-24-25 Triangle", "When learning about triangles in geometry, one key question often arises: Is a triangle with sides measuring 7 cm, 24 cm, and 25 cm a right triangle? Understanding whether a triangle is right-angled helps in solving problems related to area, angles, and applications in science, engineering, and design. In this article, we’ll explore how to determine if this triangle qualifies as a right triangle using the Pythagorean Theorem.", "### What Is a Right Triangle?", "A right triangle is defined as a triangle with one angle measuring exactly 90 degrees. In such triangles, the side opposite the right angle is called the hypotenuse—the longest side. If the square of the hypotenuse equals the sum of the squares of the other two sides, the triangle satisfies the Pythagorean Theorem:", "[\na^2 + b^2 = c^2\n]", "where ( c ) is the hypotenuse, and ( a ) and ( b ) are the other two sides.", "---", "### Applying the Pythagorean Theorem to the 7-24-25 Triangle", "Let’s assign the side lengths for clarity:", "- Side ( a = 7 ) cm\n- Side ( b = 24 ) cm\n- Side ( c = 25 ) cm (longest side, likely the hypotenuse)", "Now 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 ), this triangle satisfies the Pythagorean Theorem.", "---", "### Conclusion: Yes, It Is a Right Triangle", "The 7 cm, 24 cm, and 25 cm triangle is a right triangle because the sum of the squares of the two shorter sides equals the square of the longest side. This confirms it has a 90-degree angle, classifying it definitively as right-angled.", "---", "### Why Does This Matter?", "Recognizing right triangles is essential in fields like architecture, physics, and computer graphics, where accurate measurements and angle calculations ensure structural integrity and precise visuals. The 7-24-25 triangle is not only a classic example of a Pythagorean triple (often called a Pythagorean triple) but also a practical tool for understanding right-angle relationships in geometry.", "---", "### Summary", "- The triangle with sides 7 cm, 24 cm, and 25 cm follows the Pythagorean Theorem.\n- It meets all criteria for a right triangle: one 90° angle and ( a^2 + b^2 = c^2 ).\n- This confirms it is a right triangle — a fundamental concept reinforced through real-world applications and mathematical verification.", "---", "If you're studying geometry or preparing for exams, knowing how to check if a triangle is right-angled using the Pythagorean Theorem is crucial — and the 7-24-25 triangle is a perfect, easy-to-memorize example."]
