Question

A triangular field has sides $120m,80m$ and $50m$. Find its area. Also find the cost of fencing it with barbed wire at $rs.20$ per metre if a space of $3m$ wide is to be left for the entry gate on one of its sides. As vegetables are grown in the field for an orphanage, the fencing contractor reduced the rate of fencing by $25$. (Use$\sqrt{15}=3.88$)

Answer 1

Dimension of triangle field $\Rightarrow 120m,80m,50m$

$\Rightarrow$ perimeter = 120 + 80 + 50

$=250m$

Area = $\sqrt{125(125-120)(125-80)125-50}$

$=\sqrt{125\times 5\times 45\times 75}$

$=\sqrt{25\times 5\times 5\times 9\times 5\times 5\times 15}$

$=5\times 5\times 3\times 5\sqrt{15}$

$=375\sqrt{15}$

$=375\left(3.88\right)$

$=1455m^2$

cost of fencing = $250-3$

[perimeter of Remaining fence] = 247

Total cost $\Rightarrow 247m\times Rs20/m$

$=Rs4940.$

as the rate are reduced by 25 %

$\therefore$ new lets is $[20-20\times \frac{25}{100}]\Rightarrow 20-5=15\%$

$Rs[4950-4950\times \frac{25}{100}]$

$\Rightarrow 4950(1-\frac{1}{4})$

$4950\times \frac{3}{4}$

Final cost $\Rightarrow Rs3712.5$