An equilateral triangle is cut up into smaller equilateral triangles with side $1/6$ of the original. Find the number of triangles thus formed?

The ratio of the area of a square to that of the square drawn on its diagonal is

$A$ circle and a rectangle have the same perimeter. The sides of the rectangle are $18 \, cm$ and $26 \, cm$. What is the area of the circle? (in $cm^2$)

There are two squares $s_{1}$ and $s_{2}$. The ratio of their areas is $4:25$. If the side of $s_{1}$ is $6 \text{ cm}$,what is the side of $s_{2}$? (in $\text{cm}$)

The perimeter of a square is $48\, cm$. The area of a rectangle is $4\, cm^2$ less than the area of the square. If the length of the rectangle is $14\, cm$,then its perimeter is.......$cm$.

In the given figure,triangle $ABC$ is drawn such that $AB$ is tangent to a circle at point $A$. The radius of the circle is $10 \, cm$. The line segment $BC$ passes through the center $O$ of the circle,and point $C$ lies on the circle. If $BC = 36 \, cm$ and $AB = 24 \, cm$,what is the area (in $cm^{2}$) of triangle $ABC$?