Check: 7^2 + 24^2 = 49 + 576 = 625 = 25^2, so it is a right triangle.

Thu, 30 Apr 2026 03:07:29 +0000

Understanding the Pythagorean Theorem: Validating 7² + 24² = 25² for Right Triangle Recognition Mathematics is full of elegant patterns, and one of the most celebrated is the Pythagorean Theorem. Simple yet powerful, this theorem helps identify right triangles and deepens our understanding of geometry. One clear case involves the equation:
7² + 24² = 49 + 576 = 625, which equals 25², clearly confirming that a triangle with sides 7, 24, and 25 forms a right triangle. ### What Is the Pythagorean Theorem?
The Pythagorean Theorem states that in any right-angled triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. This means:
a² + b² = c²
where c is the hypotenuse, and a and b are the other two sides. ### Verifying the Claim: Why 7² + 24² = 25²?
Let’s break down the math step-by-step: