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# A floral design on a floor is made up of 16 tiles which are triangular, the sides of the triangle being $ 9 \mathrm{~cm}, 28 \mathrm{~cm} $ and $ 35 \mathrm{~cm} $ (see Fig. 12.18). Find the cost of polishing the tiles at the rate of $ 50 \mathrm{p} $ per $ \mathrm{cm}^{2} $

"

**Given:**

A floral design on a floor is made up of 16 tiles which are triangular, the sides of the triangle being \( 9 \mathrm{~cm}, 28 \mathrm{~cm} \) and \( 35 \mathrm{~cm} \)

**To do: **

We have to find the cost of polishing the tiles at the rate \( 50 \mathrm{p} \) per \( \mathrm{cm}^{2} \).

**Solution:**

Let the sides of the triangular tile be $a=9\ cm, b=28\ cm$ and $c=35\ cm$.

Therefore,

Using Heron's formula,

$A=\sqrt{s(s-a)(s-b)(s-c)}$

Since,

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

$S=\frac{9\ cm+28\ cm+35\ cm}{2}$

$S=\frac{72\ cm}{2}$

$S=36\ cm$

This implies,

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

$A=\sqrt{36(27)(8)(1)}$

$A=\sqrt{7,7776}\ cm^2$

$A=88.2\ cm^2$

Therefore,

The area of $16$ triangular tiles $=16\times 88.2\ cm^2$

$=1411.2\ cm^2$.

We have,

The cost of polishing the tiles $=50\ p\ per\ cm^2$

We know that,

1 Rupee $=$ 100 paise.

50 paise $=\frac{50}{100}$

$=0.5\ Rs$

Therefore,

The cost of polishing $16$ tiles at the rate of $50\ p\ per\ cm^2 =(1411.2\ cm^2\times\ Rs. 0.5)$

$=Rs.\ 705.6$

Hence,

The cost of polishing $16$ tiles at the rate of $50\ p\ per\ cm^2$ is $Rs.\ 705.6$.

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