d = \sqrt{10^2 + 24^2} = \sqrt{100 + 576} = \sqrt{676} = 26 \text{ cm}

["# Understanding the Pythagorean Theorem: How to Calculate the Hypotenuse with √676 = 26 cm", "Mathematics offers powerful tools to solve real-world problems, and one of the most foundational concepts is the Pythagorean Theorem. This classic principle allows you to determine the length of the hypotenuse in a right-angled triangle using the formula:", "[\nd = \sqrt{a^2 + b^2}\n]", "where ( a ) and ( b ) are the lengths of the two shorter sides (legs), and ( d ) is the length of the hypotenuse—the longest side opposite the right angle.", "### The Calculation: Simplifying √(100 + 576)", "Let’s break down a common example:\nCalculate ( d = \sqrt{10^2 + 24^2} )", "Start by squaring each leg:", "- ( 10^2 = 100 )\n- ( 24^2 = 576 )", "Now add the squares:", "[\nd = \sqrt{100 + 576} = \sqrt{676}\n]", "### Why √676 = 26 Centers Around Simple Roots", "The square root of 676 might seem complex at first, but it’s one of those "perfect squares" that are easy to handle:", "[\n\sqrt{676} = 26\n]", "This is because:", "[\n26 \ imes 26 = 676\n]", "Thus,", "[\nd = \sqrt{10^2 + 24^2} = \sqrt{676} = 26 \ ext{ cm}\n]", "### Real-World Applications of the Hypotenuse", "Understanding how to calculate the hypotenuse isn’t just academic—it’s practical. Whether you're:", "- Designing a diagonal support beam\n- Mapping coordinates on a grid\n- Setting up a ladder against a wall\n- Solving distance problems in physics", "the Pythagorean Theorem gives you an essential solution.", "### Final Notes", "The example ( d = \sqrt{10^2 + 24^2} = 26 \ ext{ cm} ) shows how mathematical expressions simplify cleanly using properties like perfect squares. Whether you're a student learning geometry, a DIY enthusiast, or a professional engineer, mastering this concept empowers you to measure diagonals and spatial relationships with confidence.", "Remember:\nWith a few simple steps—squaring the legs, adding, and taking the square root—you transform abstract numbers into tangible real-world measurements.", "---", "Keywords: Pythagorean theorem, hypotenuse calculation, √676, right triangle formula, 10² + 24² = 676, distance formula, geometry applications, 26 cm, square roots, real-world math, educational geometry."]