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 (see figure). Find the cost polishing the tiles at the rate of Rs.50 paise per ${cm}^2$.<br><img src="https://trustudies-app-public.s3.ap-south-1.amazonaws.com/9thmaths/12.2.8.jpg" alt="image" height="150" width="200">

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 (see figure). Find the cost polishing the tiles at the rate of Rs.50 paise per

{c m}^{2}

Answer :

Given,
the sides of a triangular tile are 9 cm, 28 cm and 35 cm.

For each triangular tile, we have,
$s = \frac{a + b + c}{2}$
$?$ $s = \frac{9 + 28 + 35}{2} = \frac{72}{2} = 36 c m$

Now, Area of triangle
= $\sqrt{36 (36 ? 9) (36 ? 28) (36 ? 35)}$
(Since, Heron's formula [area = $\sqrt{s (s ? a) (s ? b) (s ? c)}$ ])

= $\sqrt{36 \times 27 \times 8 \times 1}$
= $\sqrt{6 \times 6 \times 9 \times 3 \times 4 \times 2 \times 1}$
= $6 \times 3 \times 2 \sqrt{6} {c m}^{2}$
= $36 \sqrt{6} {c m}^{2}$
$?$ Total area of 16 such titles
= 16 × $36 \sqrt{6}$
= 16 × 36 × 2.45 ${c m}^{2}$ = 1411.20 ${c m}^{2}$

Total cost of ploshing the titles at the rate of Rs.50 paise per ${c m}^{2}$
= Rs. $\frac{50}{100} \times 1411.20$ = Rs.705.60