Question

A floral design on a floor is made up of $16$ tiles which are triangular, the sides of the triangle being $9$ cm, $28$ cm and $35$ cm. Find the cost of polishing the tiles at the rate of $50p$ per cm²

Answer 1

Step 1: Let's find area of each triangle, can be calculated by Heron’s Formula, where the sides of the triangle are given by:

$a=9cm;b=28cm;c=35cm$

By Heron’s formula :

Area of Triangle $=\sqrt{s(s-a)(s-b)(s-c)}$Square units.

Where, $s$ is the semi perimeter [which means half the perimeter of a triangle, and it is found using the formula: $s=\frac{a+b+c}{2}$]

So, Semi Perimeter,

$$\begin{gathered} s=\frac{a+b+c}{2} \\ \Rightarrow s=\frac{9+28+35}{2} \\ \Rightarrow s=36 \end{gathered}$$

Area of triangle

$$\begin{gathered} =\sqrt{s(s-a)(s-b)(s-c)} \\ =\sqrt{36(36-9)(36-28)(36-35)} \\ =\sqrt{36\times 27\times 8\times 1} \\ =36\sqrt{6}c{m}^2 \end{gathered}$$

As there are $16$ tiles, so total area

$$\begin{gathered} =16\times 36\sqrt{6} \\ =1410.906c{m}^2 \end{gathered}$$

Step 2: Let's find the cost of polishing the tiles.

Since

$\begin{array}{rcl}1c{m}^2& =& 50p=₹0.5\\ & \Rightarrow & 1410.906c{m}^2=₹0.5\times 1410.906\\ & =& ₹705.45\end{array}$

Therefore, the total polishing cost of the tiles = $₹705.6$