Question

The sides of a triangular farm are 120 m, 120 m and 192 m. What will be the expenditure of removing the grass in it at the rate of 25 ps.per square meter​

Answer 1

Given :

• The sides of a triangular farm are 120 m, 120 m and 192 m. Cost of removing the grass is 25 per m² .

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To Find :

• Expenditure of removing the grass.

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Solution :

✴ Formula Used :

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

Where :

• ➻ S = Semi - Perimeter
• ➻ a = side 1
• ➻ b = Side 2
• ➻ c = Side 3

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✴ Calculating the Area of Triangular farm :

• Semi - Perimeter :

${:\implies{\qquad{\sf{ S = \dfrac{a + b + c}{2} }}}} \\ \\ \ {:\implies{\qquad{\sf{ S = \dfrac{ 120 + 120 + 192 }{2} }}}} \\ \\ \ {:\implies{\qquad{\sf{ S = \cancel\dfrac{432}{2} }}}} \\ \\ \ {\qquad{\sf{ Semi - Perimeter \: of \: the \: farm \: = {\blue{\sf{ 216 \: m}}}}}}$

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• Area :

${:\longmapsto{\qquad{\rm{ Area = \sqrt{s (s - a) (s - b) (s - c) }}}}} \\ \\ \ {:\longmapsto{\qquad{\rm{ Area = \sqrt{216 (216 - 120) (216 - 120) (216 - 192) }}}}} \\ \\ \ {:\longmapsto{\qquad{\rm{ Area = \sqrt{216 \times 96 \times 96 \times 24 }}}}} \\ \\ \ {:\longmapsto{\qquad{\rm{ Area = \sqrt{ 12 \times 18 \times 12 \times 8 \times 12 \times 8 \times 12 \times 2 }}}}} \\ \\ \ {:\longmapsto{\qquad{\rm{ Area = 3456 \sqrt{6} }}}} \\ \\ \ {:\longmapsto{\qquad{\rm{ Area = 3456 \times 2.449 }}}} \: \: \: {\bigg\lgroup{\purple{\sf{ Taking \: \sqrt{6} = 2.449 }}} \bigg\rgroup } \\ \\ \ {\qquad{\textsf{ Area of the Triangular Farm = {\red{\sf{ 8463.8 (Approx.) }}}}}}$

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✴ Cost of Removing grass :

${:\longmapsto{\qquad{\rm{ Cost{\small_{(Removing \: Grass) }} = Area \times Rate }}}} \\ \\ \ {:\longmapsto{\qquad{\rm{ Cost{\small_{(Removing \: Grass) }} = 8463.8 \times 7 }}}} \\ \\ \ {\qquad{\textsf{ Cost of Removing grass from the field = {\green{\sf{ ₹ \: 59246.6(Approx.) }}}}}}$

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✴ Therefore :

❝ Cost of Removing the grass from the field is ₹ 59246.6 (Approx.). ❞

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Answer 2

Given :

• The three sides of the triangular farm are 120m, 120m, and 192m.
• The cost of removing the grass is 25 ps. per square meter.

to find:

• the area of the triangular firm first.

formula used :

${ \underline{ \boxed{ \bf{ \red{s = \sqrt{s(s - a)(s - b)(s - c)} }}}}}$

${ \underline{ \boxed{ \bf{ \green{s = \frac{ a+ b + c}{2} }}}}}$

Solution:

first we will use heron's formula,

here ,

• a = 120m
• b = 120m
• c = 192m.

★ semi perimeter of triangular farm

$: \implies \sf \: s=\frac{a+b+c}{2}$

$: \implies \sf \: s=\frac{120+120+192}{2}$

$\bf\pink : \implies \: s=216 \: m$

then,

★ the area of triangular farm

$\sf : \implies \: s= 216\sqrt{(216 - 120)(216 - 120)(216 - 192)}$

$\sf : \implies \: s= 6912 \: m$

Now,

• the cost of removing the grass is,

$\sf : \implies \: 6912 \: m {}^{2} \times 25 \frac{ps}{ {m}^{2} }$

$\sf : \implies \: 172800 \: ps$

$\sf : \implies \: \: rs. 1728$

hence,

• the expenditure of removing the grass is rs.1728.