A trapezium has area $1440{\text{m}}^2$ and the distance between its parallel sides is 24 m. Its two parallel sides are in the ratio 5 : 3. Find the length of the longer parallel side, in m.

Let the parallel sides be $5x$ and $3x$. Then ½ × $(5x+3x)\times 24=1440$, i.e. $96x=1440$ and $x=15$, so the sides are 75 m and 45 m. The longer one is 75 m. (Forgetting the ½ gives $x=7.5$ and a wrong 37.5 m; 1440/24 = 60 m is only the average of the two parallel sides, not the longer one.)