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 $m$)

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

Find the area of a triangle in which base is $1.5\, m$ and height is $75\, cm$? (in $sq. cm.$)

If the ratio of the areas of two squares is $9: 1$,then the ratio of their perimeters is

The length of a rectangular plot of land is three times as much as its breadth. $A$ playground measuring $1200 \ ft^2$ occupies $\frac{1}{4}$ of the total area of the plot. What is the length of the plot in feet?

What would be the cost of laying a carpet on a floor which has its length and breadth in the respective ratio of $32:21$ and where its perimeter is $212$ feet,if the cost per square foot of laying the carpet is $₹ 2.5$?