Question

A floral design on a floor is made up of $16$ tiles which are triangular, the sides of the triangle being $9cm$, $28cm$ and $35cm$ (see figure). Find the cost of polishing the tiles at the rate of $50p$ per ${cm}^2$.

Answer 1

Given:

$\Rightarrow$$a=35cm,b=28cm,c=9cm$

$\Rightarrow$Semi perimeter of tile $=\frac{a+b+c}{2}$

$\Rightarrow$Semi perimeter of tile $=\frac{35+28+9}{2}=36cm$

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

$\Rightarrow$$=\sqrt{36(36-35)(36-28)(36-9)}=\sqrt{36\times 1\times 8\times 27}$

$\Rightarrow$$=36\times 2.45=88.2{cm}^2$

$\Rightarrow$Area of total $16$ tiles $=16\times 88.2=1411.2{cm}^2$

$\Rightarrow$Cost of polishing per ${cm}^2$ area $=50p$

$\Rightarrow$Cost of polishing $1411.2{cm}^2$ area $=Rs.50\times 1411.2$ $=Rs.705.60$