Question

A plot of land has a shape of a parallelogram. It is to be covered by mud. Find the cost of speeding mud at the rate of $Rs100$ per square meter while the adjacent sides of the plot are $39m$ and $25m$ and the diagonal is $56m$ .

Answer 1

$\begin{array}{c}\&A_1=A_2\\ Areaof\parallel \left(ABCD\right)=A_1+A_2=2A_1\\ Now\Delta ABC\\ AB=39,BC=25,CA=56\\ S=\frac{a+b+c}{2}=\frac{39+25+56}{2}=60\\ Area=\sqrt{S\left(s-a\right)\left(s-b\right)\left(s-c\right)}\\ =\sqrt{60\left(60-39\right)\left(60-25\right)\left(60-56\right)}\\ =\sqrt{60\times 21\times 35\times 4}\\ =\sqrt{3\times 5\times 4\times 3\times 7\times 7\times 5\times 4}\\ =\sqrt{3\times 3\times 5\times 5\times 4\times 4\times 7\times 7}\\ =3\times 5\times 4\times 7\\ =840\\ Areaof\parallel ABCD=840\times 2\\ =1680\\ Lostofspeedingmud=1680\times 100\\ =168000\\ =Rs.1,68,000\end{array}$