Find the possible lengths of the three sides of two triangles whose perimeter is $21 \mathrm{cm}$.

$\mathrm{O}$ is the point that lies in the interior of $△\mathrm{ABC}$. Is $2\left(\mathrm{OA}+\mathrm{OB}+\mathrm{OC}\right)>$Perimeter of $△\mathrm{ABC}$.

In the given figure, $\mathrm{O}$is the center of the circle of diameter $\text{'}\mathrm{a}\text{'}$. Check which is bigger, $\text{'}3\mathrm{a}\text{'}$ or the perimeter of $△\mathrm{ABC}$.

 Given that $△\mathrm{PQR}$ is an isosceles triangle in which $\mathrm{PQ}=\mathrm{PR}$. Find the values of $\mathrm{x}$ and $\mathrm{y}$.

Find the measure of the unknown angles of the triangles in the following figure.

Are the following lengths can be the sides of a right-angled triangle?

$5, 12, 13$

Are the following lengths can be the sides of a right-angled triangle?

$6, 7, 11$

Two sides $\mathrm{AB}$ and $\mathrm{BC}$ of a right-angled triangle $\mathrm{ABC}$ right-angled at $\mathrm{B}$ are $7 \mathrm{cm}$ and $24 \mathrm{cm}$ respectively. Find the length of $\mathrm{AC}$ (in $\mathrm{cm}$).

Find the perimeter of rectangle $\mathrm{PQRS}$ from the given figure.