Let us number the vertices from 1 – 6, there are three different types of triangles that can be formed.Type 1 : (1, 2, 3) [ this is same as (2, 3, 4), (3, 4, 5) … etc)Type 2 : (1, 2, 4) [ this is same as (1, 2, 5) (2, 3, 5) (3, 4, 6)]Type 3 : (1, 3, 5) and (2, 4, 6) have same shape and area
So there will be three triangles of different areas that can be formed from a regular hexagon.There are 6 triangles of Type 1, 12 of type 2 and 2 of type 3.Adding these we get 6 + 12 + = 20 triangles.
Total number of triangles possible = 6C3 = 20
Q30) Pipe A takes 3/4 of the times required by pipe B to fill the empty tank individually. When an outlet pipe C also opened simultaneously with pipe A and pipe B it takes 3/4 more time to fill the empty tank than it takes when only pipe A and pipe B are opened together. if it takes to fill 33hrs when all the 3 pipes are opened simultaneously, then in what time pipe C can empty the full tank by operating alone.
Q100) There is a 3 digit no. ABC. The no. Is a perfect square and the no. of factors of ABC is also a perfect square.
If A + B + C is also a perfect square then what is the no of factors of the six digit number ABCABC.what is the no of factors of the 6 digit no ABCABC if the cube of the product of the digits of the no ABC is not divisible by 5?