Question

A floor is made up of 20 triangular tiles, each with sides 40 cm, 24 cm and 32 cm. Find the cost of polishing the floor at the rate of 2 rupees per sq.cm.​

Answer 1

`15360\,\,rupees`

Explanation:

Let sides of the triangle be
`a,b,c`

`a=40\,,\,b=24\,,\,c=32`

Semi-perimeter (s) =
`(a+b+c)/(2)`

`=(40+24+32)/(2)\\ =(96)/(2)\\=48`

Area of one tile
`=√(s(s-a)(s-b)(s-c))`

`=√(48(48-40)(48-24)(48-32))\\ =√(48(8)(24)(16))\\ =√(147456) \\=384\,\,cm^2`

So,

Area of 20 tiles
`=20(384)=7680\,\,cm^2`

Cost of polishing the floor at the rate of 2 rupees per sq.cm =
`7680(2)=15360\,\,rupees`