Rectangle area dimensions

We are to create a square in the shape of a rectangle with an area of 288 m² (square) so that the sides are whole numbers. What are all the dimensions of the rectangular box we can make? How many is the solution?

Final Answer:

n =  9

Step-by-step explanation:

$$\begin{gathered} 288=2\times 2\times 2\times 2\times 2\times 3\times 3=2^5\times 3^2 \\ d:1,2,3,4,6,8,9,12,16,18,24,32,36,48,72,96,144,288 \\ {S}_1=1\cdot 288=288{\text{m}}^2 \\ {S}_2=2\cdot 144=288{\text{m}}^2 \\ {S}_3=3\cdot 96=288{\text{m}}^2 \\ {S}_4=4\cdot 72=288{\text{m}}^2 \\ {S}_5=6\cdot 48=288{\text{m}}^2 \\ {S}_6=8\cdot 36=288{\text{m}}^2 \\ {S}_7=9\cdot 32=288{\text{m}}^2 \\ {S}_8=12\cdot 24=288{\text{m}}^2 \\ {S}_9=16\cdot 18=288{\text{m}}^2 \\ n=9 \end{gathered}$$

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