Question

Assertion :If lengths of two sides of a triangle are the roots of the equation $x^2-12x+35=0$ and the angle opposite to the third side is obtuse, then the square of the length of the third side is greater than $74$. Reason: In triangle $ABC$, $\cos C=\frac{a^2+b^2-c^2}{2ab}$

• A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
• B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
• C. Assertion is correct but Reason is incorrect
• D. Assertion is incorrect but Reason is correct

Answer 1

The correct option is A Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

Given, $x^2-12x+35=0$
$(x-7)(x-5)=0$
$x=7$ and $x=5$.
Now let the third side be $y$.
Hence
$\cos Y=\frac{7^2+5^2-y^2}{2(7\times 5)}$
$=\frac{49+25-y^2}{70}$.
Now if $Y$ is obtuse, then $cosY<1$.
$\frac{49+25-y^2}{70}<1$
$y^2>74$.