Exploring the Pythagorean Theorem with a 3-4-5 Triangle: Properties and Applications

3-4-5 triangle

A 3-4-5 triangle is a right triangle with side lengths of 3, 4, and 5 units

A 3-4-5 triangle is a right triangle with side lengths of 3, 4, and 5 units. In any right triangle, the sum of the squares of the two smaller sides is equal to the square of the longest side. This property is known as the Pythagorean Theorem.

In the case of a 3-4-5 triangle, we can check if it satisfies the Pythagorean theorem.

The two smaller sides are 3 and 4. We can calculate their squares:
3^2 = 9
4^2 = 16

Now let’s calculate the square of the longest side, which is 5:
5^2 = 25

To verify if this triangle is a 3-4-5 triangle, we need to check if the sum of the squares of the two smaller sides (9 + 16 = 25) is equal to the square of the longest side (25).

Since 9 + 16 equals 25, the Pythagorean theorem is satisfied, and this triangle is indeed a 3-4-5 triangle.

The significance of a 3-4-5 triangle is that it is one of the simplest and most commonly used right triangles. The ratio of the side lengths (3:4:5) is a Pythagorean triple, which means that the lengths of the sides are whole numbers and satisfy the Pythagorean theorem. This property makes 3-4-5 triangles easy to work with in calculations and applications of geometry and trigonometry.

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