Q. 194.3( 24 Votes )

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. Find the cost of polishing the tiles at the rate of 50p per cm2.


Answer :

To Find: Cost of polishing of tiles

Given: Sides of the triangle are 9 cm, 28 cm, and 35 cm.


Cost of polishing of tiles is 50p per cm2.


Concept Used:


If sides of a triangle are a, b, and c, then area of a triangle is given by:



Where s = semiperimeter of the triangle



Diagram:


Let us look at one of the triangles:



Explanation:


Now we can see that all triangles are congruent.


Therefore,


Area of Design = 16 × Area of one triangle.




s = 36 cm





Area = 36√6 cm2


Area of 16 tiles = 16 × 36√6 cm2 = 576√6 cm2


Cost of polishing = 0.5 × Area in cm2


Therefore,


Total cost of polishing = Rs. 0.5 × 576√6 = Rs. 705.45


[Take √6 = 2.45]


Hence, the total cost of polishing is Rs. 705.45


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