If the area of a triangle is $150 \, m^{2}$ and the ratio of the base and the height is $3:4$,then find its height in $m$.

How many times will a wheel of diameter $105\, cm$ rotate in covering a distance of $330\, m$? (in $revolutions$)

$ABC$ is a triangle. $AB = 5 \text{ cm}$,$AC = \sqrt{41} \text{ cm}$,and $BC = 8 \text{ cm}$. $AD$ is perpendicular to $BC$. What is the area (in $\text{cm}^2$) of triangle $ABD$?

Height of an equilateral triangle is $6 \, cm$. Find its side? (in $cm$)

The length of a rectangle is thrice its breadth and its perimeter is $96 \, m$. The area of the rectangle is......$m^2$

The length of a rectangle is increased by $60 \%$. By what percent would the width have to be decreased so as to maintain the same area?