The height of an equilateral triangle whose perimeter is $24 \, cm$ is

If the area of a square increases by $69 \%$,then the side of the square increases by (in $\%$)

In the given figure,$ABCD$ is a square. $EFGH$ is a square formed by joining the midpoints of the sides of $ABCD$. $LMNO$ is a square formed by joining the midpoints of the sides of $EFGH$. $A$ circle is inscribed inside $LMNO$. If the area of the circle is $38.5 \text{ cm}^2$,then what is the area (in $\text{cm}^2$) of square $ABCD$?

$A$ rectangular sheet of cardboard is of $4 \, cm \times 2 \, cm$. If a circle of the greatest possible area is cut from it,then the area of the remaining portion is:

The sides of a right-angled triangle forming the right angle are in the ratio $5: 12$. If the area of the triangle is $270 \, cm^2$,then the length of the hypotenuse is .......... $cm$.

The perimeter of an isosceles triangle is $14 \ cm$. The lateral side and the base are in the ratio $5:4$. The area of the triangle in $cm^2$ is: