Question

Assertion (A) : The set of all real numbers ‘$a$' such that $a^2+2a,2a+3,a^2+3a+8$ are sides of a triangle is $(5,\infty )$.
Reason (R) : In a triangle, sum of two sides is greater than the third side and sides are positive.

• A. Both (A) & (R) are individually true & (R) is correct explanation of (A)
• B. Both (A) & (R) are individually true but (R) is not the correct (proper) explanation of (A)
• C. (A) is true but (R) is false
• D. (A) is false but (R) is true

Answer 1

Answer: (A)

$a^2+2a>0,a\in (-\infty ,-2)\cup (0,\infty )$
Also, $2a+3>0,a\in (-3/2,\infty )$
$a^2+3a+8>0\forall a\in R$
Now, $2a^2+5a+8>2a+3$
$\Rightarrow 2a^2+3a+5>0\forall a\in R$
Also, $a^2+5a+11>a^2+2a$
$\Rightarrow 3a+11>0$
$\Rightarrow a>-11/3$
$a^2+4a+3>a^2+3a+8$
$\Rightarrow a-5>0$
$\Rightarrow a>5$
So, $a\in (5,\infty )$
(By combining all the equations)