Question

The number of isosceles triangles with integer sides such that no side is greater than $4$ units is

• A. $8$
• B. $9$
• C. $16$
• D. $12$

Answer 1

The correct option is A $8$

Let the sides be x, x, y condition $1\le x,y\le 4$

We know sum of $2$ sides greater than $3^{rd}$ side

x, x, y

$4$ $4$ $(1,2,3)$ $\Rightarrow 3$ solutions

$3$ $3$ $1,2,4$ $\Rightarrow 3$ solutions

$2$ $2$ $1,3$ $\Rightarrow 2$ solutions

$1$ $1$ $x$

_____________________________

$8$ solutions

$\therefore$ No. of isosceles triangle $=8$ triangles.