On the basis of the length of their sides triangles can be classified into three types:
1. Scalene triangle: The triangles having all their sides of different lengths are known as scalene
2. Isosceles triangle: The triangles that have two of their sides equal in length are known as isosceles
3. Equilateral triangle: They have all the three sides equal in length to each other.
Example 1: Identify the following triangles as scalene, isosceles or equilateral triangle.
a. Triangle PQR with sides PQ = 15 cm, QR = 15 cm, RA = 15 cm.
b. Triangle DEF with sides DE = 11 inches, EF = 10 inches, FD = 11 inches.
c. Triangle ABC with sides AB = 5 cm, BC = 7 cm, CA = 6 cm.
a. The lengths of all the three sides of the triangle are equal. Thus triangle PQR is equilateral.
b. Since the lengths of two sides DE and FD are equal to each other, thus triangle DEF is isosceles.
c. In triangle ABC all the sides are of different lengths, so this triangle is scalene.
Example 2: The sum of the three sides of triangle XYZ is 36 cm. If YZ = 12 cm, ZX = 13 cm then what type of
triangle is XYZ?
Solution: It is given that the sum of the three sides of a triangle is 36 cm.
Thus, XY+YZ+ZX = 36
XY+12+13 = 36
XY+25-25 = 36 - 25
XY = 11
Since the length of all the sides of triangle XYZ is different, this triangle is scalene.