Question

the area of a rectangular garden is 1729 square feet. List all possible whole-number dimensions the garden can have

Answer 1

$$\begin{gathered} \mathrm{The}\mathrm{prime}\mathrm{factorisation}\mathrm{of}1729\mathrm{is}7\times 13\times 19 \\ \mathrm{So},\mathrm{the}\mathrm{possible}\mathrm{whole}\mathrm{number}\mathrm{dimension}\mathrm{of}\mathrm{rectangle}\mathrm{are}: \\ \left(7\times 13\right)\times 19=91\mathrm{ft}\times 19\mathrm{ft} \\ \left(19\times 13\right)\times 7=247\mathrm{ft}\times 7\mathrm{ft} \\ \left(7\times 19\right)\times 13=133\mathrm{ft}\times 13\mathrm{ft} \\ \left(7\times 13\times 19\right)\times 1=1729\mathrm{ft}\times 1\mathrm{ft} \end{gathered}$$