Question

A floral design on a floor is made up of 10 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 1

Answer:

Step-by-step explanation:

Answer 2

Answer :-

• Total cost of polishing 10 tiles = 441 ₹

Given :-

• Total Number of Tiles = 10
• First Side of Triangular Tile = 9 cm
• Second Side of Triangular Tile = 28 cm
• Third Side of Triangular Tile = 35 cm
• Rate of Polishing the Tiles = 50 paise / cm²

To Find :-

• Total Cost of Polishing the Tiles the 10 Tiles.

Explanation :-

In order to Find the cost of Polishing 10 Tiles, First we need Find the cost of polishing 1 Tile. We will use Heron's Formulae To find the area of Tiles.

$\underline { \boxed { \bf \longrightarrow Heron's \: Formulae = \sqrt{s (s - a) (s - b) (s - c)} }}$

Where,

• s = Semi-Perimeter of Triangle
• a = First Side of Triangle
• b = Second Side of Triangle
• c = Third Side of Triangle

$\boxed { \bf \longrightarrow Semi \: Perimeter = \dfrac{Perimeter}{2} }$

$\rm \implies \dfrac{9 + 28 + 35}{2} \: cm$

$\rm \implies \dfrac{72}{2} \: cm$

$\bf \implies 36 \: cm$

Now, Substituting the values

$\bf Area \: of \: 1 \: tile = \sqrt{s (s-a) (s-b) (s-c)}$

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

$\rm \longrightarrow \sqrt{36 \times 8 \times 27 \times 1}$

$\rm \longrightarrow 36\sqrt{6}$

$\rm \longrightarrow 36 \times 2.44$

$\boxed { \bf \longrightarrow 88.2 \: cm^2 \quad (Approx.) }$

$\rm \therefore \; \; Area \: of \: 10 \: Tiles = (88.2 \times 10) \: cm^2 \\ \qquad \qquad \quad = 882 \: cm^2$

$\rm \implies Rate \: of \: Polishing \: Tiles = 50 \: Paise / cm^2$

$\rm \implies Total \: Cost \: of \: Polishing \: Tiles = (882 \times 0.5) \: Rs$

$\underline { \boxed { \rm \implies Total \: Cost \: of \: Polishing = 441 Rs }}$

Hence, the total cost of polishing the tiles is 441 ₹

@Agamsain