Question

The edges of a triangular board are 41 cm, 40cm and 9 cm. The cost of painting one surface of the board at the rate of Rs 6 per sq cm is​

Answer 1

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Answer 2

Given:

The edges of a triangular board $a,\;b,\;and\;c$ are $41\;cm,\;40\;cm\;and\;9\;cm$

The cost of painting per square cm = Rs: $6$

To find:

The cost of painting one surface of the board

Formula:

$S\;=\;\frac{a+b+c}2$ where S is the semi-perimeter

Area of the triangle = $\sqrt{s(s-a)\;(s-b)\;(s-c)}$ square units

Step-by-step explanation:

$S\;=\;\frac{41\;+\;40\;+\;9}2$

$S\;=\;\frac{90}2\;=\;45\;cm$

Δ = $\sqrt{s(s-a)(s-b)(s-c)}$

Δ = $\sqrt{45(45-41)(45-40)(45-9)}$

Δ = $\sqrt{45\;\times\;4\;\times5\;\times36}$

Δ = $3\;\times\;5\;\times\;2\;\times\;6$

Δ = $180$ $cm^{2}$

The cost of painting one surface of the board = $180\;\times\;6$ = Rs: $1080$

Answer:

Therefore, the cost of painting one surface of the board at the rate of Rs: $6$ per sq cm is​ Rs: $1080$