Question

The edges of a triangular board are 6 cm, 8 cm and 10 cm. The cost of painting it at the rate of Rs.5 per sq.cm is

Answer 1

AnswEr:-

Your Answer Is 120 Rupees.

ExplanaTion:-

Given:-

• Edges of a triangle = 6cm, 8cm and 10 cm.

• Cost of painting per sq cm = Rs 5.

To Find:-

• The cost of painting the whole triangle.

Formula Used:-

Heron's Formula,

$\bf\longrightarrow A = \sqrt{s(s - a)(s - b)(s - c)} .$

Where,

• A = Area of a triangle.

• s = Semi Perimeter of the triangle.

• a, b and c = Three edges of the triangle respectively.

So Here,

• A = ?? [To Find].

• a = 6 cm.

• b = 8 cm.

• c = 10 cm.

$\tt\leadsto s = ( \dfrac{6 + 8 + 10}{2} )cm$

$\tt\leadsto s = (\dfrac{24}{2}) \: cm$

$\bf\leadsto\boxed{ \bf s = 12 \: cm.}$

Now,

Lets put the above values in the formula:-

$\tt\mapsto A = \sqrt{s(s - a)(s - b)(s - c)} .$

$\tt = \sqrt{12(12 - 6)(12 - 8)(12 - 10)} \: \: cm {}^{2} .$

$\tt = \sqrt{12(6)(4)(2)} \: \: cm {}^{2} .$

$\tt = \sqrt{(72)(8)} \: \: cm {}^{2} .$

$\tt = \sqrt{576} \: \: cm {}^{2}.$

$\boxed{\bf = 24 \: cm {}^{2}}$

So The Area of the given triangle is 24 cm².

Now,

$\because$ Cost of painting 1 m² = Rs 5.

$\therefore$ Cost of painting 24 cm²,

= Rs (24 × 5).

= Rs 120.

Therefore the total cost of painting the given triangular board is 120 Rupees.