Question

If the size of the ground area is $6 \,\text{km \times 3 \,\text{km}$ and the corresponding photo size in the aerial photograph is $30 \,\text{cm} \times 15 \,\text{cm}$, then the scale of the photograph is $1 : \underline{\hspace{3cm}}$ (in integer).}

Hint:

In aerial photo scale problems, always convert ground distances into the same unit as the photograph (cm). Then use $\text{Scale} = \dfrac{\text{Photo distance}}{\text{Ground distance}}$.

Answer 1

Step 1: Convert ground distances to cm.
Ground size: $6 \,\text{km} \times 3 \,\text{km}$.
\[ 6 \,\text{km} = 6000 \,\text{m} = 6000 \times 100 \,\text{cm} = 600000 \,\text{cm} \] \[ 3 \,\text{km} = 3000 \,\text{m} = 3000 \times 100 \,\text{cm} = 300000 \,\text{cm} \]

Step 2: Compare photo size with ground size.
On the photo: $30 \,\text{cm} \times 15 \,\text{cm}$.
On the ground: $600000 \,\text{cm} \times 300000 \,\text{cm}$.
Scale ratio: \[ \frac{\text{Photo length}}{\text{Ground length}} = \frac{30}{600000} = \frac{1}{20000} \] \[ \frac{\text{Photo width}}{\text{Ground width}} = \frac{15}{300000} = \frac{1}{20000} \]

Step 3: Final scale.
Thus the photograph scale is: \[ 1 : 20000 \] \[ \boxed{1 : 20000} \]