Question

The altitude and the base of a triangular field are in the ratio 6 : 5. If its cost is Rs 49,57,200 at the rate of Rs 36,720 per hectare and 1 hectare =10,000 sq. m, find (in metre) dimensions of the field.

Area of the given triangular field $=\frac{Costofthefield}{Rate}=\frac{49,57,200}{36,720}$ hectare

=135 hectare

$=135\times 10,000$ sq. m=1350000 $m^2.$

Answer 1

Total cost =Rs 49,57,200

Rate =Rs 36,720 per hectare

$\therefore$ Total area of the triangular field

$=\frac{4957200}{36720}\times 10000m^2=1350000m^2$

Ratio in altitude and base of the field =6 :5

Let altitude =6x and base =5x

$\therefore$ Area $=\frac{1}{2}$ Base $\times$ Altitude

$\Rightarrow 1350000=\frac{1}{2}\times 5x\times 6x$

$\Rightarrow 15x^2=1350000\Rightarrow x^2=\frac{1350000}{15}$

$\Rightarrow x^2=90000=(300{)}^2$

$\therefore x=300$

$\therefore$ Base =5x=5 $\times$ 300=1500 m and altitude $=6x=6\times 300=1800m$