Question

On a map, drawn to a scale of 1 : 2,50,000; a triangular plot of land has the following measurements : AB = 3 cm, BC = 4 cm and angle ABC = ${90}^{\circ }$. Calculate : (i) the actual lengths of AB and BC in km. (ii) the area of the plot in sq. km.

Answer 1

Scale:-1 : 250000

∴ 1 cm represents 250000cm

= $\frac{250000}{1000\times 100}$

= 2.5

(i)

Actual length of AB = $3\times 2.5$ = 7.5 km

Actual length of BC = $4\times 2.5$ = 10 km

The actual length of AC = $\sqrt{{7.5}^2+{10}^2}$ = 12.5 Km

2nd-

Area of ABC = $\frac{1}{2}AB\times BC$

= $\frac{1}{2}\times 3\times 4$ = $6c{m}^2$


1cm represents 2.5 Km
$1c{m}^2$ represents $2.5\times 2.5k{m}^2$
The area of plot = $2.5\times 2.5\times 6$ = 37.5 $k{m}^2$