The base and height of a right-angled triangle are $5\text{cm} \text{and} 12\text{cm}$ respectively. Find the third side and draw the right-angled triangle.

A semicircular paper is folded along a chord such that the folded circular arc is tangent to the diameter of the semicircle. The radius of the semicircle is $4$ units and the point of tangency divides the diameter in the ratio $7:1.$ If the length of the crease (the dotted line segment in the figure) is $l$ then determine $l^2.$

Let $ABC$ be a triangle such that $AB=6\sqrt{3}cm$, $AC=12 cm$, and $BC=6 cm$. Angle $B$ is 

In the following figure, all the vertically opposite angles formed are right angles. The perimeter of the coplanar figure is _____

$a,b,c$ are the sides of $∆ABC$. If $\text{'}a\text{'}$ is the length of the longest side of $∆ABC$, from the following, _____pair is true to determine the type of $∆ABC$.

Pairs:

$\left(1\right) a^2>b^2+c^2$                         $\left(x\right)$ right angled triangle

$\left(2\right) a^2<b^2+c^2$                         $\left(y\right)$ obtuse angled triangle.

$\left(3\right)$ $a^2=b^2+c^2$                         $\left(z\right)$ acute angled triangle  

A chord $AB$ of length $20\mathrm{cm}$ is at a distance of $4\mathrm{cm}$ from the center $O$ of a circle.

The perimeter of a square $ABCD$ is $32$. Then the measure of its diagonal $AC=$ _____.