Question

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

Answer 1

Area of the triangular field $=\frac{Costofthefield}{Rate}=\frac{49,57,200}{36,720}=135hectares$
Since, $1hectare=10000sqm;135hectares=135\times 10000=1350000sqm$
Let the altitude of the triangle be $6x$ and the base be $5x$ .

Area of triangle $=\frac{1}{2}\times base\times height=1350000$

$=>\frac{1}{2}\times 6x\times 5x=1350000$ sq m

$x^2=90000$ m

$x=300$ m

Hence, altitude of the triangle be $6x=1800m$ and the base be $5x=1500m$ .