A triangle has sides of lengths 7 cm, 24 cm, and 25 cm. Determine if it is a right triangle using the Pythagorean theorem.

Sun, 03 May 2026 04:35:50 +0000

**A triangle has sides of lengths 7 cm, 24 cm, and 25 cm. Determine if it is a right triangle using the Pythagorean theorem.** In a world where shapes shape perception—from design principles to everyday problem solving—many pause when confronted with a triangle measuring 7, 24, and 25 centimeters. Does this combination truly form a right triangle? The Pythagorean theorem offers a clear mathematical lens to explore this, drawing attention from homeowners, students, and DIY enthusiasts alike. With growing interest in geometry, architecture, and spatial reasoning, this triangle stands out not just as a shape—but as a gateway to understanding foundational math in real life. Do 7, 24, and 25 form a right triangle? According to the Pythagorean theorem, a triangle is right-angled if the square of the longest side equals the sum of the squares of the other two sides. For these measurements, the longest side is 25. Checking the math: 7² + 24² equals 49 + 576 = 625, and 25² equals exactly 625. With perfect alignment, this triangle satisfies the theorem—confirming it is indeed a right triangle. This striking result invites deeper curiosity. Real-world applications span architecture and construction, where right-angled triangles ensure structural integrity and safety. From trusses in homes to precision tools, knowing whether a triangle is right helps professionals and hobbyists alike. The 7-24-25 combination—though often overshadowed by the 3-4-5 benchmark—holds clean, simple proportions ideal for teaching foundational math or verifying design dimensions quickly.