Question

the edge of a triangular board are 6cm,8cm,10cm calculate the cost of painting it as the rate of 9paise per cm²
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Answer 1

Given edges of the triangular board = 6 cm , 8 cm and 10 cm .

So the dimensions are :

a = 6 cm

b = 8 cm

c = 10 cm

We have to find the cost of painting it on the rate of 9 paise / cm² .

But first we will have to find the area to be painted .

Finding the area to be painted by using Heron's formula :

Semi perimeter of the triangle = (a+b+c)/2 = (6+8+10)/2 = 24/2 = 12 cm

Then , the area =

$\sqrt{(s)(s - a)(s - b)(s - c)} \\ \\ \sqrt{(12)(12 - 6)(12 - 8)(12 - 10)} \\ \\ \sqrt{12 \times 6 \times 4 \times 2} \\ \\ 12 \times 2} = 24 \: {cm}^{2}$

So the required area to be painted = 24 cm²

Total cost required = 24 × 9 = 216 paise = ₹2.16

Answer 2

Solution:-

Dimensions of Triangular Board are 6cm , 8cm & 10cm.

To Find out the Area of Triangular Board, we need to Find the Semi perimeter of the Triangular Board.

=> S = (a + b + c)/2

=> S = 24/2 = 12.

Now, Area of The Triangular Board;

=> √s (s-a) (s-b) (s-c)

=> √ 12 (12-6) (12-8) (12-10)

=> √ 12× 6 × 4× 2

=> √ 6 × 2 × 6 × 4 × 2

=> 6 × 2 × 2

=> 24cm².

Cost of Painting for 1 cm² = ₹0.09

=> Cost of Painting for 24cm² = 24 × 0.09

=> Cost of Painting for 24 cm²= ₹ 2.16.