Question

$ABC$ is a triangle such that $AB=10$ and $AC=3$. The side $BC$ is:

• A. $=7$
• B. $>7$
• C. $<7$
• D. None of these

Answer 1

The correct option is B $>7$

In $\Delta ABC,AB=10,AC=3$
In a triangle, the sum of any two sides is always greater than the third side.
$\left(i\right)AB+BC>AC\left(ii\right)BC+AC>AB$ and

$\left(iii\right)AB+AC>BC$
Also, the difference of any two sides is less than the third side.
$\left(i\right)BC\sim AB<AC\left(ii\right)AC\sim BC<AB$ and

$\left(iii\right)(AC\sim AB)<BC$

$\therefore BC>AC\sim AB\Rightarrow BC>7$ and

$(10+3)>BC13>BC$
$\therefore BC<13$