Question

The number of isoseles 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 $8$

$\because$ the triangle is isoseles let the sides be $X,x,y.$

Max value of $x$ is $4$

Also sum of any two sides of $△$ is greater than $3rd$ sides.

For $x=4$, $Y$ can take value from $1$ to $3.$

For $x=3$ $y$ can be $(6,2,4)$

For $x=2$ $Y$ can be $(1,3)$

For $x=1$ ${\rm Y}$ has no case

So, total ${△}^{\prime }s=3+3+2$

$=8$

Hence, the answer is $8.$