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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 (see the given figure). Find the cost of polishing the tiles at the rate of 50p per cm2.
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Solution
It can be observed that
Semi-perimeter of each triangular-shaped tile,
`s=(35+28+9)/2=36cm`
By Heron’s formula,
`"Area of triangle "=sqrt(s(s-a)(s-b)(s-c))`
`"Area of each tile "=[sqrt(36(36-35)(36-28)(36-9))]cm^2`
`=[sqrt(36xx1xx8xx27)]cm^2`
`=36sqrt6 cm^2`
= (36 x 2.45) cm^2
= 88.2 cm2
Area of 16 tiles = (16 × 88.2) cm2= 1411.2 cm2
Cost of polishing per cm2 area = 50 p
Cost of polishing 1411.2 cm2 area = Rs (1411.2 × 0.50) = Rs 705.60
Therefore, it will cost Rs 705.60 while polishing all the tiles.
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