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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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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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