Question

On a map drawn to scale of 1 : 2,50,000 a rectangular plot of land ABCD has the following measurement AB = 12 cm, BC = 16 cm angles A, B, C, and D are 90⁰ each. Calculate:
(i) The diagonal distance of the plot of land in
(ii) Actual length of diagonal.

Answer 1

(i) Here k = `(1)/(2,50,000)`

Length of diagonal (on map)
= `sqrt("AB"^2 + "BC"^2)`
= `sqrt(12^2 + 16^2)`
= `sqrt(400)`
= 20 cm
(ii) Length of diagonal on map
= k x Actual length of the diagonal
⇒ 20 = `(1)/(2,50,000) xx "Actual length of the diagonal"`
⇒ Actual length of diagonal
= 20 (2,50,000) cm
= 5000000 cm
= 50 km.