The longest side in a right-angled triangle is called the hypotenuse. It is always opposite the right angle.
Here's why:
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Pythagorean Theorem: The Pythagorean Theorem states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides (legs). This relationship ensures that the hypotenuse is always the longest side.
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Visual Representation: Imagine a right-angled triangle where the legs are 3 units and 4 units long. Using the Pythagorean Theorem, the hypotenuse would be √(3² + 4²) = 5 units. This clearly demonstrates that the hypotenuse is longer than both legs.
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Practical Applications: Understanding the hypotenuse is crucial in various fields like construction, engineering, and navigation. For example, when calculating the length of a ladder needed to reach a certain height on a wall, the ladder represents the hypotenuse, and the wall and ground represent the legs of the right-angled triangle.
In summary, the hypotenuse is the longest side in a right-angled triangle because it is opposite the right angle and its length is determined by the Pythagorean Theorem.
