Question

A floral desing 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

We have lengths of the sides of 1 triangular tile.

$a=9cm$

$b=28cm$

$c=35cm$

$s=\frac{a+b+c}{2}=\frac{9+28+35}{2}$

$=36cm$

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

$=\sqrt{36\left(36-9\right)\left(36-28\right)\left(36-35\right)}$

$=\sqrt{36\times 27\times 8\times 1}$

$=\sqrt{6\times 6\times 3\times 3\times 3\times 4\times 2}$

$=6\times 3\times 2\sqrt{6}$

$=36\sqrt{6}c{m}^2$

Area of 16 tiles $=16\times 36\sqrt{6}$

$=576\sqrt{6}$

Cost of polishing $=576\sqrt{6}\times \frac{50}{100}$

$=288\sqrt{6}$

$=705.45$ Rs.