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Need clarity, kindly explain! Let S be the set of all triangles in the xy-plane,each having one vertex at the origin and the other two vertices lie on coordinate axes with integral coordinates. If each triangles is S has area 50 sq. units, then the number

Let S be the set of all triangles in the xy-plane,each having one vertex at the origin and the other two vertices  lie on coordinate axes with integral coordinates. If each triangles is S has area 50 sq. units, then the number of the elements in the set S is:

  • Option 1)

     

    9

  • Option 2)

     

    32

  • Option 3)

     

    18

  • Option 4)

     

    36

Answers (1)
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A admin

 

Number of Divisions -

The number of divisors of a natural number 

n=(a_{1})^{k_{1}}(a_{2})^{k_{2}}..............(a_{m})^{k_{m}} is 

(k_{1}+1)(k_{2}+1)..........(k_{m}+1)

- wherein

Where a1, a2 ....... are distinct prime and non negative integers.

 

 

Let A = (\alpha, 0)

and B = (0, \beta) be vectors of \DeltaAOB\Delta AOB

Area of \Delta le is \\= \frac{1}{2}\times base \times height \\ = \frac{1}{2}\times \alpha \times \beta = 50

|\alpha\beta| = 50\times 2 =100

Number of triangles 

= 4\times (number \;of\; divisions\;100) = 4\times 9= 36

 


Option 1)

 

9

Option 2)

 

32

Option 3)

 

18

Option 4)

 

36

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