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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