question_answer

 

Directions: Each of these questions contains two statements: Assertion [A] and Reason [R]. Each of these questions also has four alternative choices, any one of which is the correct answer. You have to select one of the codes [a], [b], [c] and [d] given below.

Assertion Points A(6, 4), B(- 4, - 6) and C (4, 6) are such that\[AB=\sqrt{200}\],

\[BC=\sqrt{208},\,AC=\sqrt{8}\].

Since, AB + BC > AC, points A,B and C form a triangle.

Reason If \[B{{C}^{2}}=A{{B}^{2}}+A{{C}^{2}}\], then \[\Delta ABC\]is a right triangle, right angled at A.

A) A is true, R is true; R is a correct explanation for A.

B) A is true, R is true; R is not a correct explanation for A.

C) A is true; R is False.

D) A is false; R is true.

Correct Answer: B

Solution :

\[\therefore \,\,AB+BC>AC\] and \[AB+AC>BC\]

\[\therefore \,\,ABC\]is a triangle

[\[\because\]Sum of the two sides is greater than third side]

Also, \[B{{C}^{2}}=A{{B}^{2}}+A{{C}^{2}}\]

\[\left[ \because \,\,{{\left( \sqrt{208} \right)}^{2}}={{\left( \sqrt{200} \right)}^{2}}+{{\left( \sqrt{8} \right)}^{2}} \right]\]

\[\therefore\] ABC is a right angled triangle.

Assertion is true Reason is true but is not the correct explanation of Assertion.