Question

In the figure above, $AC=7$ and $AB=BC$. Find the smallest possible integer value of $AB$.

• A. $4$
• B. $5$
• C. $6$
• D. $7$
• E. $9$

Answer 1

The correct option is A $4$

We know, third side rule of triangle states that, third side of a triangle is less than the other two sides of triangle,
Here in triangle $ABC$, let $AC$ be the third side, $AB$ and $BC$ be the other two sides.
Let $AB$ and $BC$ be $x$, as $AB=BC$
As per rule,
$7<x+x$
$\Rightarrow 7<2x$
$\Rightarrow x>3.5$
Since $x>3.5$, smallest possible value of $x$ will be $4$.