Question

A triangle park in a city has dimensions $110m\times 100m\times 90m$. A gardener has to plants grass inside the park at the rate of $Rs3.50$ per $m^2$. Find the amount to be paid to gardener?

Answer 1

We have,

The sides of triangular park is $110\times 100\times 90$

So,

$a=110m.$

$b=100m.$

$c=90m.$

Now, Parameter

$s=\frac{a+b+c}{2}$

$s=\frac{110+100+90}{2}$

$s=\frac{300}{2}$

$s=150cm$

Now,

Area of triangle$=\sqrt{s(s-a)(s-b)(s-c)}$

$Areaof\Delta =\sqrt{150(150-110)(150-100)(150-90)}$

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

$=\sqrt{15\times 4\times 5\times 6\times 100\times 100}$

$=\sqrt{60\times 30\times 100\times 100}$

$=\sqrt{18\times 100\times 100\times 100}$

$=10\times 10\times 10\sqrt{18}$

$=1000\times 3\sqrt{2}$

$=3000\sqrt{2}$

$=3000\times 1.414$

$=4242m^2$

Now,

Cost

$=4242\times 3.50$

$=Rs14847$

Hence, this is the answer.