Question

On a map drawn to a scale of 1:25000, a rectangular plot of land has sides 12cm x 16cm. Calculate: The diagonal distance of the plot in km

Answer 1

scale = 1:25000
In rectangle ABCD,
AB = 12cm,BC = 16cm
AC is the diagonal.
By Pythagoras theorem
AC² = AB² + BC²
AC² = 12² + 16²
AC² = 144 + 256 = 400
⇒ AC = 20cm
∵ Scale = 1:25000
AC = 20 x 25000cm

⇒ AC = `(20 xx 25000)/(100 xx 1000)`km
⇒ AC = 5km.