Question

A 5.25 m by 3.78 m rectangular courtyard is to be paved with square tiles of the same size such that only tiles are used. What is the largest possible size of such a tile? Also find the number of tiles required.

Answer 1

$$\begin{gathered} \mathrm{Given}: \\ \mathrm{Length}=5.25\mathrm{m}=525\mathrm{cm} \\ \mathrm{Breadth}=3.78\mathrm{m}=378\mathrm{cm} \\ \mathrm{The}\mathrm{HCF}\mathrm{of}\mathrm{the}\mathrm{length}\mathrm{and}\mathrm{breadth}\mathrm{is}21. \\ \mathrm{Hence},\mathrm{the}\mathrm{side}\mathrm{of}\mathrm{the}\mathrm{tile}\mathrm{is}21\mathrm{cm}. \\ \therefore \mathrm{Number}\mathrm{of}\mathrm{tiles}=\frac{\mathrm{Area}\mathrm{of}\mathrm{the}\mathrm{courtyard}}{\mathrm{Area}\mathrm{of}\mathrm{the}\mathrm{tile}} \\ =\frac{525\times 378}{21\times 21} \\ =\frac{198450}{441} \\ =450 \end{gathered}$$