On a photograph of a triangular piece of land, the lengths of the three sides are $12 \mathrm{~cm}, 15 \mathrm{~cm}$, and $21 \mathrm{~cm}$ respectively. The shortest side of the actual piece of land is $240 \mathrm{~m}$ long. Find the lengths of the other two sides.
The side of the piece of land corresponding to the side of length $15 \mathrm{~cm}$ in the photograph is $\mathrm{m}$ long. (Simplify your answer. Type an integer or decimal.)
The side of the piece of land corresponding to the side of length $21 \mathrm{~cm}$ in the photograph is $\mathrm{m}$ long. (Simplify your answer. Type an integer or decimal.)

Step 1 ：Given that the shortest side of the actual piece of land is 240 meters and corresponds to the shortest side in the photograph which is 12 cm, we can find the scale factor by dividing the actual length by the photograph length. This gives us a scale factor of \(\frac{240}{12} = 20\).

Step 2 ：We can then use this scale factor to find the lengths of the other two sides of the actual piece of land. The side of the piece of land corresponding to the side of length 15 cm in the photograph is \(15 \times 20 = 300\) meters long.

Step 3 ：Similarly, the side of the piece of land corresponding to the side of length 21 cm in the photograph is \(21 \times 20 = 420\) meters long.

Step 4 ：Final Answer: The side of the piece of land corresponding to the side of length 15 cm in the photograph is \(\boxed{300}\) meters long. The side of the piece of land corresponding to the side of length 21 cm in the photograph is \(\boxed{420}\) meters long.