Determine if the given side lengths could be used to form a unique triangle, many different triangles, or no triangles.

4 m, 5.1 m, 12.5 m

A.

unique triangle

B.

many different triangles

C.

no triangles

no triangles

Step-by-step explanation:

As we know the basic rule to form a triangle is that the sum of the two sides must be greater than the third one.

Given that:

4 m, 5.1 m, 12.5 m

We have: 4 m + 5.1 m = 9.1 m < 12.5 m

So no triangles can be formed.

Answer: The given side lengths could be used to form A: Unique triangle

Step-by-step explanation: The dimensions given are 4 m, 5.1 m, and 12.5 m.

With three sides already provided, we can deduce a triangle can be formed, and to determine if its a right angled triangle or not, we shall apply the Pythagoras theorem to prove.

The Pythagoras theorem states that the sum of the squares of the two sides equals to the square of the longest side (hypotenuse) in a right angled triangle. In other words, it is expressed as follows;

AC² = AB² + BC²

Where AC is the longest side (hypotenuse) and AB and BC are the other two sides. We can now write it out properly as;

12.5² = 5.1² + 4²

156.25 = 26.01 + 16

156.25 ≠ 42.01

As we can see from the calculations shown, the three dimensions of the triangle does not satisfy the Pythagoras theorem and can not be used to form a right angled triangle.

The given dimensions can only be used to form a unique triangle such that the derived angles would also be unique and once changed would equally change the lengths of the given dimensions.