Exploring the Properties and Applications of the 3-4-5 Triangle in Geometry and Construction

3-4-5 triangle

A 3-4-5 triangle refers to a right triangle in which the lengths of the sides are in the ratio of 3:4:5

A 3-4-5 triangle refers to a right triangle in which the lengths of the sides are in the ratio of 3:4:5. In other words, if the length of one of the shorter sides is 3 units, the length of the other shorter side is 4 units, and the length of the longest side (the hypotenuse) is 5 units.

This particular type of triangle is known as a Pythagorean triple because it follows the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. In the case of a 3-4-5 triangle, if you square the length of the shorter sides and add them together, you will get the square of the length of the hypotenuse.

To illustrate, if we designate the shorter sides as “a” and “b”, and the hypotenuse as “c”, we can apply the Pythagorean theorem:

a^2 + b^2 = c^2

For a 3-4-5 triangle:

3^2 + 4^2 = 5^2

9 + 16 = 25

25 = 25

This equation is true, indicating that the lengths of the sides of a 3-4-5 triangle follow the Pythagorean theorem.

The 3-4-5 triangle is useful in geometry and construction because it allows for easy measurement and calculation. It can be used to create accurate right angles and serves as a basis for scaling larger or smaller right triangles.

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