Question

An old map was plotted on a scale of 40 m to 1 cm. Over the year, this map has been shrinking and a line originally 20 cm long is only 19.5 cm long at present. Again, the 20 m chain was 5 cm too long. If the present area of the map measured by planimeter is 125.50 $c{m}^2$, then the true area of land surveyed is ______ hectares.

• A. 21.23

Answer 1

The correct option is A 21.23
19.5 cm on the map was originally 20 cm,
$\therefore 1c{m}^2\text{on the map was originally}$

$=\frac{{20}^2}{{19.5}^2}c{m}^2$

$\Rightarrow 125.50c{m}^{2}wasoriginally$

$\frac{{20}^2}{{19.5}^2}\times 125.50=132.0184c{m}^2$

$\because \text{Scale of map was 1 cm = 40 m}$

$\Rightarrow 1c{m}^2=1600m^2$

$\Rightarrow Areaontheground=1600\times 132.0184$
$=211,229.44m^2$

Since the chain was 0.05 m too long.

$\therefore Truearea=\frac{{20.05}^2}{{20}^2}\times \frac{211229.44}{{10}^4}=21.23hectares$