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A floral design on a floor is made up of...

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 `50` paise per `cm^(2)`.

A

`Rs. 790.60`

B

`Rs. 705.60`

C

`Rs. 675.60`

D

`Rs. 780.60`

Text Solution

Verified by Experts

The correct Answer is:
B
Given, the sides of a triangular tiles are `9 cm, 28 cm` and `35 cm.`
For each triangular tile, we have
`s=(9+28+35)/(2)=(72)/(2)`
`rArr s=36 cm`
`:.` Area of each triangular tile ` = sqrt(36(36-9)(36-28)(36-35)) " " ` (by Heron's formula)
` = sqrt(36xx27xx8xx1)`
`=sqrt((6)^(2)xx(3)^(2)xx3xx(2)^(2)xx2)=36 sqrt(6) cm^(2)`
`:.` Total are of 16 such tiles `=16xx36xxsqrt(6) cm^(2)`
` =16xx36xx2.45 cm^(2) = 1411.20 cm^(2)`
Total cost of polishing the tiles at the rate of `50` paise per `cm^(2)`
`=Rs. (50)/(100)xx1411.20=Rs. 705.60`
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