Can We Draw a Triangle with Sides 15cm, 20cm, and 25cm? Exploring the Possibilities

When considering the construction of a triangle with specific side lengths, one of the fundamental principles is the triangle inequality theorem. This theorem ensures that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. By applying this rule, we can determine if it is possible to draw a triangle with sides measuring 15 cm, 20 cm, and 25 cm.

Applying the Triangle Inequality Theorem

To verify if a triangle can be drawn with these side lengths, we need to check the following conditions:

Condition 1: a b > c Condition 2: a c > b Condition 3: b c > a

Let's apply these conditions to the given side lengths of 15 cm, 20 cm, and 25 cm:

Verification of Conditions

Condition 1: 15 cm 20 cm > 25 cm 35 cm > 25 cm (True) Condition 2: 15 cm 25 cm > 20 cm 40 cm > 20 cm (True) Condition 3: 20 cm 25 cm > 15 cm 45 cm > 15 cm (True)

Since all three conditions are satisfied, we can confidently state that a triangle with sides measuring 15 cm, 20 cm, and 25 cm can indeed be constructed.

Additional Properties of the Triangle

Not only can this triangle be drawn, but it also has some interesting properties. For instance, this specific triangle adheres to the 3:4:5 ratio, which means it is a right triangle. This can be verified through the Pythagorean theorem:

Verifying the Right Triangle

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. Let's apply this to our triangle:

152 202 225 400 625 252

Since the equation holds true, we can conclude that this triangle is a right triangle with a hypotenuse of 25 cm and legs of 15 cm and 20 cm.

Conclusion

Given the triangle inequality theorem and the properties of the 3:4:5 ratio, we can draw a triangle with sides measuring 15 cm, 20 cm, and 25 cm. This triangle not only meets the requirements for being a valid triangle but also has the additional characteristic of being a right triangle. Understanding these principles is crucial for anyone working with geometric shapes and their properties.