Two roads $XY$ and $YZ$ of $15 \ m$ and $20 \ m$ length respectively are perpendicular to each other. What is the distance between $X$ and $Z$ by the shortest route? (in $m$)

If the length of a rectangle is increased in the ratio $6:7$ and its breadth is diminished in the ratio $5:4$,then its area will be changed in the ratio:

The area of a triangular lawn is $1600 \, m^{2}$. If one side is $64 \, m$ long and the other two sides are equal in length,the length of each equal side is......$m$

$\Delta ABC$ is similar to $\Delta PQR$. The length of $AB$ is $16 \ cm$ and the length of the corresponding side $PQ$ is $9 \ cm$. If the area of $\Delta ABC$ is $1024 \ cm^2$,what is the area of $\Delta PQR$ in $cm^2$?

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

How many tiles,each $4 \, dm$ square,will be required to cover the floor of a room $8 \, m$ long and $6 \, m$ broad?