The perimeter of equilateral $\Delta ABC$ is $30$. Find its area. (in $\sqrt{3}$)

The lengths of the diagonals of a rhombus are $10$ and $24$. Then,the length of each side of the rhombus is $\ldots \ldots \ldots \ldots . .$

In a rectangle $ABCD$,if $AB^{2} + BC^{2} = 64$,then find the length of the diagonal $AC$.

In rhombus $ABCD$,$AC = 18$ and $BD = 24$. Find the perimeter of rhombus $ABCD$.

Sides of triangles are given below. Determine which of them are right triangles. In case of a right triangle,write the length of its hypotenuse.
$50 \text{ cm}, 80 \text{ cm}, 100 \text{ cm}$

In $\Delta ABC$,$A-M-B$,$A-N-C$ and $\overline{MN} \parallel \overline{BC}$. If $AM = x+1$,$MB = x$,$AN = 3x-3$ and $NC = 4x-10$,then $x = \dots$