Question

The edges of a triangular board are 6cm, 8cm & 10cm. The cost of painting it at the rate of Rs 5per cm2 is
Choose the correct option from given below
(A)
Rs 200
(B)
Rs 300
(C)
Rs 120
(D)
Rs 248

Answer 1

Given :-

The edges of a triangular board are 6cm, 8cm & 10cm. The cost of painting it at the rate of Rs 5per cm2

To Find :-

Cost of painting

Solution :-

We know that

Semi-perimeter = a + b + c/2

Semi-perimeter = 6 + 8 + 10/2

Semi-perimeter = 24/2

Semi-perimeter = 12 cm

Now, By using heron's formula

Area = √s(s - a)(s - b)(s - c)

Area = √12(12 - 6)(12 - 8)(12 - 10)

Area = √12  × 6 × 4 × 2

Area = 2 × √(12 × 6 × 2)

Area = 2 × √(144)

Area = 2 × 12

Area = 24 cm²

Now Finding cost

Cost = Area × Rate

Cost = 24 × 5

Cost = Rs 120

Therefore, Option C is correct

Answer 2

Given: The edges of a triangluar Board are 6 cm, 8 cm and 10 cm. & The cost of painting it at the rate of Rs 5 per cm².

Need to find: The Cost of painting?

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❍ Let's say, that the sides of triangle be x, y and z are 6 cm, 8 cm & 10 cm respectively.

⌑ We'll use Heron's formula to find out the area of the given triangular Board. First we'll calculate semi – perimeter of the triangle —

» Semi - perimeter is Given by Sum of all sides of triangle —

$:\implies\sf S = \Bigg\{\dfrac{x + y + z}{2}\Bigg\}$

$:\implies\sf S = \Bigg\{\dfrac{6 + 8 + 10}{2}\Bigg\}$

$:\implies\sf S = \cancel\dfrac{24}{2}$

$:\implies{\boxed{\pmb{\frak{S = 12\;cm}}}}$

$\therefore{\underline{\textsf{Hence, Semi-perimeter of the triangle is \textbf{12 cm.}}}}$

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✇ Now, Calculating area of the triangluar board —

⠀

$\star\;\underline{\pmb{\boxed{\sf{Area_{\:(triangle)} = \sqrt{s\Big(s - a\Big)\Big(s - b\Big)\Big(s - c\Big)}}}}}$

$:\implies\sf Area_{\:(triangle)} = \sqrt{12\Big(12 - 6\Big)\Big(12 - 8\Big)\Big(12 - 10\Big)}$

$:\implies\sf Area_{\:(triangle)} = \sqrt{12\times 6 \times 4 \times 2}$

$:\implies\sf Area_{\;(triangle)} = \sqrt{576}$

$:\implies\underline{\boxed{\pmb{\frak{Area_{\:(triangle)} = 24\;cm^2}}}}\;\bigstar$

$\;\;\;\therefore{\underline{\sf{Hence,\; Area\; of \;the\; triangle \;is \;{\pmb{\sf{24\;cm^2}}}.}}}$

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» Now, we've to find out the cost of painting the board at rupees 5 per cm². So, Let's Solve :

⠀

$\longrightarrow{ \pmb{\mathbb{ COST = RATE \times AREA }}}$

$\longrightarrow\sf Cost = 5 \times 24$

$\longrightarrow\underline{\boxed{\pmb{\frak{\purple{Cost = 120}}}}}\;\bigstar$

$\therefore{\underline{\sf{Hence,\; the \;Cost\; of\; painting \;is~ {\pmb{\sf{Option~ c)~120~ rs}}}.}}}$