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Statement-1: Let x(1),x(2),x(3),y(1),y(...

Statement-1: Let `x_(1),x_(2),x_(3),y_(1),y_(2) andy_(3) ` be integers and `A(x_(1),y_(1)),B(x_(2),y_(2)) and C(x_(3),y_(3))` be three non-collinear points. Then `DeltaABC` is not equilateral.
Statement-2: Area of an equlateral trinalge is `(sqrt(3))/(4) ("Side")^(2)`

A

Statement-1 is True, Statement-2 is True, Statement-2 is a correct explanation for Statement-1

B

Statement-1 is True, Statement-2 is True, Statement-2 not a correct explanation for Statement-1

C

Statement-1 is True, Statement-2 is False.

D

Statement-1 is False, Statement-2 is True

Text Solution

Verified by Experts

The correct Answer is:
A
Clearly, statement-2 is true,
Let the triangle be equilateral. Then,
Area of `DeltaABC-(sqrt(3))/(4)("Side")^(2)=` An irrationla number.
Also,
Area of `Delta ABC`= Absolut vlue of `(1)/(2)|{:(x_(1),y_(1),1),(x_(2),y_(2),1),(x_(3),y_(3),1):}|`
`rArr` Area of `DeltaABC=` rational number
Thus, we have,
A rational number = An irrational numbers.
This is not possible. So, `DeltaABC` is not equilateral.
Hence, statement-1 is true
Also, statement-2 is the correct explanation for staement-1
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