Question

The size of a triangular field are 165cm ,143cm and 154 cm . Find the cost of painting it at 12paise per sq .cm.

Answer 1

AnswEr :

• Sides of Triangular Field are 165cm, 143cm and 154cm.
• Find Cost of Painting @12paise/cm²

we will find out the Area of Triangle with the help of Heron's Formula :

⋆ a = 165cm ; b = 143cm and c = 154cm

⇒ Semi Perimeter = Sum of Sides ÷ 2

⇒ s = (a + b + c) ÷ 2

⇒ s = (165 + 143 + 154) ÷ 2

⇒ s = 462 ÷ 2

⇒ s = 231

⠀

$\longrightarrow \large \sf{Ar. \: of \: \triangle = \sqrt{s(s - a)(s - b)(s - c)} }$

$\longrightarrow \sf{Ar. \: of \: \triangle = \sqrt{231(231 - 165)(231 - 143)(231 - 154)} }$

$\longrightarrow \sf{Ar. \: of \: \triangle = \sqrt{231 \times 66 \times 88 \times 77}}$

$\longrightarrow \small\sf{Ar. \: of \: \triangle = \sqrt{(7 \times 3 \times 11) \times (2 \times 3\times 11) \times (2 \times 2 \times 2 \times 11) \times( 7 \times 11)}}$

$\longrightarrow \sf{Ar. \: of \: \triangle = 7 \times11 \times 11 \times 3 \times 2 \times 2 }$

$\longrightarrow \boxed{\sf{Ar. \: of \: \triangle =10164 \: {cm}^{2} }}$

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• Cost of Painting of the Triangular Field :

⇒ Cost = Area of Field × Rate

⇒ Cost = 10,164 cm² × 12 paise

⇒ Cost = 121,968 paise

⇒ Cost = Rs. (121,968 ÷ 100)

⇒ Cost = Rs. 1219.68

⇒ Cost = Rs. 1220⠀ [Approx]

⠀

჻ Cost of Painting of field is Rs. 1220

Answer 2

Question:-

The size of a triangular field are 165cm ,143cm and 154 cm . Find the cost of painting it at 12paise per sq .cm .

Answer:-

To Find:-

Find cost.

Formula used :-

$\star \: \sf{area \: of \: \triangle \: } \\ = \sf{ \sqrt{s(s - a)(s - b)(s - c)} } \\ \:$

Step - by - step explanation :-

Given that :-

Let,

• a =165 cm, b =143 cm ,c =154 cm

Firstly we have to find area of triangle to find the cost .

We know that,

Semi perimeter (S) = ( Sum of sides ) / 2

→ S = ( 165 + 143 + 154 ) / 2

→ S = 462 /2

→ S = 231

Now ,using the given formula for for area of triangle ,

$= \small \: \sqrt{231(231 - 165)(231 - 143)(231 - 154)} \\ \\ = \sqrt{231 \times 66 \times88 \times 77 } \\ \\ = \small \sqrt{(7 \times 3 \times 11)(2 \times 3 \times 11)(2 \times 2 \times 2 \times 11)(7 \times 11)} \\ \\ = 2 \times 2 \times 3 \times 7 \times 11 \times 11 \\ \\ \boxed{ \sf{area \: of \: \triangle= 10164 \: {cm}^{2} }}$

Now ,

For find the cost,

• Rate = ₹ 12 / sq.cm

We know that,

→ Cost = Area of field × Rate

→ Cost = 10164 × 12( Paise)

→ Cost = 121968 paise

→ Cost = Rs(1219.68 )