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.
A 3-4-5 triangle is a right triangle with the sides in the ratio of 3:4:5. In other words, the length of the shortest side is 3 units, the length of the next shortest side is 4 units, and the length of the longest side (opposite the right angle) is 5 units.
This specific triangle is of great importance in mathematics and engineering due to the simplicity of its sides’ ratio. For example, the Pythagorean theorem can easily be applied to find the length of the hypotenuse or either of the other two sides.
To find the length of the hypotenuse, we can use the Pythagorean theorem which states that the square of the length of the hypotenuse equals the sum of the squares of the other two sides. In this case, that would be:
5^2 = 3^2 + 4^2
Simplifying this equation, we get:
25 = 9 + 16
Therefore, the length of the hypotenuse is the square root of 25, which is 5.
Similarly, we can find the length of the other two sides by rearranging the Pythagorean theorem. For example, to find the length of the shorter leg, we can use:
3^2 = 5^2 – 4^2
Simplifying this equation, we get:
9 = 25 – 16
Therefore, the length of the shorter leg is the square root of 9, which is 3.
In summary, the 3-4-5 triangle is a right triangle that has sides in the ratio of 3:4:5. This triangle is important in mathematics and engineering due to its simplicity and the ease at which its sides can be calculated using the Pythagorean theorem.
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