Question

A floral design on a floor is made up of 12 tiles which are triangular, the sides of the triangle being 9 cm, 28 cm and 35 cm (see figure). Find the cost of polishing the tiles at the rate of 50 p per cm2.

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Answer 1

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A floral design on a floor is made up of 12 tiles which are triangular, the sides of the triangle being 9 cm, 28 cm and 35 cm (see figure). Find the cost of polishing the tiles at the rate of 50p per cm².

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Given :-

• Triangular tiles.
• Sides :- 28cm, 9cm, 35cm.
• Cost of polishing tiles = 50p per cm²

To find :-

• Cost of polishing the tiles.

Let :-

• a = 28 cm
• b = 9 cm
• c = 35 cm

Before finding cost, first we have to find area of all floral tiles.

Semiperimeter of a tile

$\color{green} \bold{\boxed{ \implies \frac{a + b + c}{2}}}$

$\implies \frac{28 + 9 + 35}{2}$

$\implies \frac{72}{2}$

$\color{lime}\implies36 \: cm$

Therefore, semeperimeter of tile is 36 m.

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Area of triangle = We will find the area by Heron's formula

$\color{green} \bold{\boxed{ \mathtt{{ \sqrt{s(s - a)(s - b)(s - c)}}}}}$

$\implies\sqrt{36(36 - 35)(36 - 9)(36 - 28)}$

$\implies \sqrt{36 \times 1 \times 8 \times 27}$

$\implies \sqrt{2 \times 2 \times 3 \times 3 \times 1 \times 2 \times 2 \times 2 \times 3 \times 3 \times 3}$

$\implies2 \times 3 \times2 \times 3 \sqrt{1 \times 2 \times 3}$

$\implies36 \sqrt{6}$

$\implies36×2.45</strong><strong>$

$\color{lime}\implies88.2 \: {cm}^{2}$

Area of triangle is 88.2 cm².

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Area of total 16 tiles

$\implies16 \times 88.2$

$\color{lime}\implies1411.2  \: {cm}^{2}$

Therefore, area of 16 tiles is 1411.2 cm².

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Cost of polishing all the tiles:-

$\implies \: Rs \: 50×1411.2$

$\color{brown} \bold{ \boxed{ \mathtt{\implies \: Rs. 705.60}}}$

Therefore, cost of polishing all the 16 tiles are Rs 705.60.

Answer 2

Answer:

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