Question

A triangular park in a city has dimensions $100m\times 90m\times 110m$. A contract is given to a company for planting grass in the park at the rate of $Rs.4000$ per. hectare. Find the amount to be paid to the company. (Take $\sqrt{2}=1.414$) (1 hectare $=10,000m^2$)

• A. $Rs.1696.8$
• B. $Rs.1596.8$
• C. $Rs.1600.8$
• D. $Rs.1486.8$

Answer 1

The correct option is A $Rs.1696.8$

Area of triangle $=\frac{a+b+c}{2}$ is $\sqrt{s(s-a)(s-b)(s-c)}$.
For triangle with sides 100 m, 90 m and 110 m, $s=\frac{100+90+110}{2}=150m$
Area of the triangle $=\sqrt{150(150-100)(150-90)(150-110)}$

$=\sqrt{150\times 50\times 60\times 40}$

$=\sqrt{50\times 3\times 50\times 20\times 3\times 20\times 2}$

$=50\times 20\times 3\sqrt{2}$

$=3000\sqrt{2}{m}^2$

$=3000\times 1.414=4242m^2$

$=\frac{4242}{10000}$ hectare

Cost of planting grass in the park at the rate of $Rs.4000$ per. hectare $=\frac{4242}{10000}\times Rs.4000=Rs.1696.8$