Certainly! Let's determine the side lengths for each type of triangle:
a. Scalene Triangle: A scalene triangle has all sides of different lengths.
To form a scalene triangle:
- [tex]\( AB = 3 \)[/tex]
- [tex]\( BC = 4 \)[/tex]
- [tex]\( AC = 5 \)[/tex]
In this case, all three sides are of different lengths, thus forming a scalene triangle.
b. Equilateral Triangle: An equilateral triangle has all sides of equal lengths.
To form an equilateral triangle:
- [tex]\( AB = 6 \)[/tex]
- [tex]\( BC = 6 \)[/tex]
- [tex]\( AC = 6 \)[/tex]
Each side is equal, satisfying the condition for an equilateral triangle.
c. Isosceles Triangle: An isosceles triangle has two sides of equal length and the third side of a different length.
To form an isosceles triangle:
- [tex]\( AB = 7 \)[/tex]
- [tex]\( BC = 7 \)[/tex]
- [tex]\( AC = 5 \)[/tex]
Here, two sides ([tex]\( AB \)[/tex] and [tex]\( BC \)[/tex]) are of equal length, and the third side ([tex]\( AC \)[/tex]) is different, forming an isosceles triangle.
In conclusion, the lengths for each type of triangle are:
- For the scalene triangle: [tex]\( AB = 3 \)[/tex], [tex]\( BC = 4 \)[/tex], [tex]\( AC = 5 \)[/tex]
- For the equilateral triangle: [tex]\( AB = 6 \)[/tex], [tex]\( BC = 6 \)[/tex], [tex]\( AC = 6 \)[/tex]
- For the isosceles triangle: [tex]\( AB = 7 \)[/tex], [tex]\( BC = 7 \)[/tex], [tex]\( AC = 5 \)[/tex]
These values ensure that each triangle fits its respective classification.
