A triangle has sides of lengths 7 cm, 24 cm, and 25 cm. Verify if it is a right triangle and find its area.

Wed, 06 May 2026 06:01:43 +0000

**A triangle has sides of lengths 7 cm, 24 cm, and 25 cm. Verify if it is a right triangle and find its area.** Why are so many people exploring triangles with side lengths 7 cm, 24 cm, and 25 cm right now? This familiar set of measurements sparks curiosity because they form one of the most recognized Pythagorean triples. Common in math classrooms and online discussions, this triangle combination offers a simple yet powerful example of fundamental geometry principles. Whether learners are brushing up on basic concepts or investigating real-world applications, understanding whether this triangle is right-angled and how to calculate its area opens doors to broader insights about shapes, proportions, and spatial reasoning. Is this triangle a right triangle? To confirm, apply the Pythagorean theorem: the square of the longest side (hypotenuse) must equal the sum of the squares of the other two sides. For a triangle with sides 7 cm, 24 cm, and 25 cm, check:
25² = 625
7² + 24² = 49 + 576 = 625
Since both sides match, this triangle is indeed a right triangle, with 25 cm as the hypotenuse. This straightforward validation reinforces foundational geometry skills crucial for students, hobbyists, and professionals alike. Calculating the area follows logically from the right angle: multiply half the base by half the height, then double it. Since the legs are 7 cm and 24 cm, the area is:
Area = (1/2) × 7 × 24 = 84 square centimeters.
This offers not just a numerical result but a practical lesson in applying geometry to real-life contexts—such as design, construction, or data visualization—where understanding spatial dimensions supports informed decision-making.