Question

On a map drawn to a scale of $1:50,000$, a rectangular plot of land ABCD has the following dimensions. AB$=6$cm; BC$=8$cm and all angles are right angles. Find the actual length of the diagonal distance AC of the plot in km.

Answer 1

$AB=6cm,BC=8cm$

According to pythagoras theorem

$\Rightarrow AC=\sqrt{A{B}^2+B{C}^2}$

$\Rightarrow AC=\sqrt{6^2+8^2}$

$\Rightarrow AC=\sqrt{36+64}=\sqrt{100}=10cm$

On the map the length of the diagonal of the plot is $10cm$.

Thus, the actual length will be $50,000\times 10=500,000cm=5km$

(Since $1km=100,000cm$).