Question

The number of triangles with any three of the lengths 1, 4, 6, and 8 cm is
A). One
B). Two
C). Three
D). Four

Answer 1

Hint: Before attempting these types of questions, one should have prior knowledge about the basic rules for the construction of a triangle such as the sum of 2 sides of a triangle should not be less than the third side, using this information can help you to approach the solution of the problem.

Complete answer:
According to the question, we are given the four lengths that are 1, 4, 6, and 8. So, the following combination of sides of the triangle are as follows
Case I:
1cm, 4cm, 6cm since here the sum of two sides is less than the third side therefore the triangle cannot be formed
Case II:
1cm, 6cm, 8cm since here the sum of two sides is less than the third side therefore the triangle cannot be formed
Case III:
1cm, 4cm, 8cm since here the sum of two sides is less than the third side therefore the triangle cannot be formed
Case IV:
4cm, 6cm, 8cm since here the sum of two sides is more than the third side therefore the triangle cannot be formed
Hence only one triangle can be formed with sides 4cm, 6cm, 8cm
Therefore, only one triangle can be formed by the given dimensions
Hence, option A is the correct option.

Note: In the above questions, we came across the term triangle which can define as the polygon which consists three sides having three vertices there are different types of triangles such as the isosceles triangle in which 2 sides are equal to each other, equilateral triangle where every side is equal to each other, right angle triangle where one angle is equal to $90^{\circ}$, etc.