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If S is a set of triangles whose one ver...

If S is a set of triangles whose one vertex is origin and other two vertices are integral coordinates and lies on coordinate axis of area 50 square units, then number of elements in set S is equal to (a) 9 (b) 18 (c) 36 (d) 40

A

36

B

32

C

18

D

9

Text Solution

Verified by Experts

The correct Answer is:
A
According to given information, we have the following figure.

(Note that as a and b are integers so they can be negative also). Here O(0, 0), A(a, 0) and B(0, b) are the three vertices of the triangle.
Clearly, `OA = |a| " and " OB = |b|`.
`therefore` Area of `DeltaOAB = 1/2 |a||b|.`
But area of such triangles is given as 50 sq units.
`therefore` `1/2 |a||b| = 50`
`rArr` `|a||b| = 100 = 2^(2) * 5^(2)`
Number of ways of distributing two 2's in `|a|` and `|b| = 3`

`rArr 3` ways
Similarly, number of ways of distributing two 5's in `|a|` and `|b|` = 3 ways.
`therefore` Total number of ways of distributing 2's and 5's `= 3 xx 3 = 9` ways
Note that for one value of `|a|`, there are 2 possible values of a and for one value of `|b|` there are 2 possible values of b.
`therefore` Number of such triangles possible `= 2 xx 2 xx 9 = 36`.
So, number of elements in S is 36.
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