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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 cm, 28 cm and 35 cm (see Fig. 12.18). Find the cost of polishing the tiles at the rate of 50p per cm 2 .

Q8.    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 Fig. 12.18). Find the cost of polishing the tiles at the rate of 50p per cm2.

                

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GIven the sides of the triangle are:

a = 9\ cm,\ b = 28\ cm\ and\ c= 35\ cm.

So, its semi-perimeter will be:

s = \frac{a+b+c}{2} = \frac{9+28+35}{2} = 36\ cm

Therefore, the area of the triangle using Heron's formula is given by,

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

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

= \sqrt{7776} \approx 88.2\ cm^2

So, we have the area of each triangle tile which is 88.2\ cm^2.

Therefore, the area of each triangular 16 tiles will be:

= 16\times 88.2\ cm^2 = 1411.2\ cm^2

Hence, the cost of polishing the tiles at the rate of 50 paise per cm2 will be:

= Rs.\ 0.50\times1411.2\ cm^2 =Rs.\ 705.60

 

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