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 cm^{2}.

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 cm^{2}.

**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 cm^{2}

Area of 16 tiles = 16 × 36√6 cm^{2} = 576√6 cm^{2}

Cost of polishing = 0.5 × Area in cm^{2}

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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