If the area of a triangle with base $x$ is equal to the area of a square with side $x,$ then the altitude of the triangle is

The ratio of bases of two triangles is $x: y$ and that of their areas is $a: b$. Then the ratio of their corresponding altitudes will be

In a triangle $ABC$,$AB + BC = 12 \text{ cm}$,$BC + CA = 14 \text{ cm}$,and $CA + AB = 18 \text{ cm}$. Find the radius of the circle (in $\text{cm}$) which has the same perimeter as the triangle.

$A$ square has an area of $200\, m^2$. $A$ new square is formed such that the length of its diagonal is $\sqrt{2}$ times the diagonal of the given square. What is the area of the new square in $m^2$?

$A$ rectangle has width $a$ and length $b$. If the width is decreased by $20 \%$ and the length is increased by $10 \%$,what is the area of the new rectangle as a percentage of the original area $ab$?

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 $\text{cm}$)