Exploring The Pythagorean Theorem: The 3-4-5 Triangle And Its Proof

3-4-5 triangle

a triangle in which the sides are 3, 4, and 5 units long. A 3-4-5 triangle is always a right triangle.

The 3-4-5 triangle is a right triangle where the lengths of the legs are 3 units and 4 units, and the length of the hypotenuse is 5 units. It is called a 3-4-5 triangle because these numbers satisfy the Pythagorean theorem which states that in any right triangle, the square of the hypotenuse (the longest side) equals the sum of the squares of the other two sides.

To prove that the 3-4-5 triangle satisfies the Pythagorean theorem, we can use the formula c^2 = a^2 + b^2, where c is the length of the hypotenuse and a and b are the lengths of the legs.

Plugging in the values for the 3-4-5 triangle, we get:

c^2 = 3^2 + 4^2
c^2 = 9 + 16
c^2 = 25

Taking the square root of both sides, we get:

c = sqrt(25)
c = 5

Therefore, the length of the hypotenuse in a 3-4-5 triangle is indeed 5 units, which satisfies the Pythagorean theorem.

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