Question

a land is in the form of a triangle with side of the land are 18 24 and 30 find the cost of levelling the land at the rate for of rupees 30 per square metre.​

Answer 1

Answer:

✴ Given :

A land is the shape of a triangle with sides 18 m, 24 m and 30 m. Cost of levelling is 30 per m² .

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✴ To Find :

Total cost of levelling.

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✴ Solution :

$\begin{gathered}{\orange{\sf{Solution }}} \begin{cases} & \sf{Concept} \\ \\ & \sf {Formula \: Used } \\ \\ & \sf { Area{\small_{(Triangle) }}} \\ \\ & \sf { Cost{\small_{(Levelling) }} }\end{cases} \end{gathered}$

✏ Concept :

As we have been given the sides of the triangle and we know levelling is done in the area. So, we will find the area using formula Area of triangle .We will get the area and than we can easily calculate total cost by by multiplying the area with cost of levelling 1 m².

$\qquad{━━━━━━━━━━━━━━━━━━━━━━━━━━}$

✏ Formula Used :

$\large{\orange{\bigstar}} \: \: {\underline{\boxed{\red{\sf{ Area{\small_{(Triangle) }} = \sqrt{s(s - a) (s - b) (s - c) }}}}}}$

Where :

➳ S = Semi - Perimeter

➳ A = Side 1

➳ B = Side 2

➳ C = Side 3

$\qquad{━━━━━━━━━━━━━━━━━━━━━━━━━━}$

✏ Area of Triangular land :

Semi - perimeter :

$\qquad{:\implies{\sf{ S = \dfrac{ a + b + c}{2}}}}$

$\qquad{:\implies{\sf{ S = \dfrac{ 18 + 24 + 30}{2}}}}$

$\qquad{:\implies{\sf{ S = \cancel\dfrac{ 72}{2}}}}$

$\qquad \: \: \: {\large{\blue{\longrightarrow{\underline{\pink{\sf{36 \: cm}}}}}}}$

$\qquad{:\implies{\sf{ Area{\small_{(Triangle)}} = \sqrt{s( s - a) (s - b) (s - c)} }}}$

$\qquad{:\implies{\sf{ Area{\small_{(Triangle)}} = \sqrt{36( 36 - 18) (36- 24) (36 - 30)}}}}$

$\qquad{:\implies{\sf{ Area{\small_{(Triangle)}} = \sqrt{36 \times 18 \times 12 \times 6} }}}$

$\qquad{:\implies{\sf{ Area{\small_{(Triangle)}} = \sqrt{6 \times 6\times 6 \times 3 \times 6 \times 2 \times 6 \times 1} }}}$

$\qquad{\large{\red{:\implies}}\: \: \:{\underline{\boxed{\purple{\sf{216 \: cm² }}}}}}{\red{\bigstar}}$

$\qquad{━━━━━━━━━━━━━━━━━━━━━━━━━━}$

✏ Cost of Levelling :

${:\implies{\sf{ Cost\:of\:levelling{\small_{(1 \: m²)}} = ₹ 30}}}$

${:\implies{\sf{ Cost\:of\:levelling{\small_{(216 \: m²)}} = 30 \times 216}}}$

$\qquad{\large{\red{:\implies}}\: \: \:{\underline{\boxed{\purple{\sf{₹ \: 6480 }}}}}}{\red{\bigstar}}$

$\qquad{━━━━━━━━━━━━━━━━━━━━━━━━━━}$

Therefore :

❝ Cost of levelling the triangular field is ₹ 6480. ❞

${\purple{\underline{\orange{▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬}}}}$