Question

A gardener has to put double fence all around the triangular field of side 120m, 80m and 60m . In the middle of each side there is a gate of width 10 m . Find the rate of fencing at the rate of rs. 6/m.
guys it is urgent please help
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Answer 1

Answer :-

$\: \: \boxed{\boxed{\rm{\mapsto \: \: \: Firstly \: let's \: understand \: the \: concept \: used}}}$

Here the concept of Perimeter of the Triangle has been used. According to this, if we calculate the perimeter of the triangle, we can get the total cost of fencing. First of all, we will add all the sides from where we will subtract the width of the gates on each side. Then we can multiply the length we got into the fence twice for double fencing. Let's do it  !!

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★ Formula Used :-

$\: \: \\ \large{\leadsto \: \: \: \boxed{\boxed{\sf{Perimeter \: of \: Triangle \: = \: \bf{Sum \: of \: all \: the \: sides}}}}}$

$\: \large{\leadsto \: \: \: \: \: \sf{Length \: of \: field \: to \: be \: fenced \: = \: \bf{2 \: \times \: [Perimeter \: of \: field \: - \: 3(Width \: of \: gate)]}}}$

$\: \\ \large{\leadsto \: \: \: \boxed{\boxed{\sf{Total \: cost \: of \: fencing \: = \: \bf{Perimeter \: of \: field \: to \: fenced \: \times \: Rate \: of \: fencing}}}}}$

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★ Question :-

A gardener has to put double fence all around the triangular field of side 120m, 80m and 60m . In the middle of each side there is a gate of width 10 m . Find the rate of fencing at the rate of rs. 6/m.

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★ Solution :-

Given,

» Sides of Triangular Field (△) = 120 m, 80 m and 60 m

» Width of each gate = 10 m

Since, the gate is in the middle of each side and every gate is of same length, we can simply multiply it with 3 and subtract its value from the perimeter of triangular field.

Then, according to the question :-

~ For Perimeter of the Field :-

$\: \: \large{\longrightarrow \: \: \: \: \: \sf{Perimeter \: of \: Triangle \: = \: \bf{Sum \: of \: all \: the \: sides}}}$

➣ Perimeter of the△field = 120 m + 80 m + 60 m

➣ Perimeter of△field = 260 m

$\: \\ \large{\boxed{\boxed{\tt{Perimeter \: \: of \: \: Triangular \: \: field \: \: = \: \bf{260 \: m}}}}}$

~ For Length of Triangular Field to be fenced :-

$\: \large{\longrightarrow \: \: \: \: \: {\sf{Length \: of \: field \: to \: be \: fenced \: = \: \bf{2 \: \times \: [Perimeter \: of \: field \: - \: 3(Width \: of \: gate)]}}}}$

➣ Length of△field to be fenced = 2 × [260 - 3(10)]

(Here we are multiplying with 2 because we need to double fence the Triangular Field. So length to be fenced will be twice)

➣ Length of△field to be fenced = 2 × [260 - 30]

➣ Length of△field to be fenced = 2 × 230

➣ Length of△field to be fenced = 460 m

$\: \\ \large{\boxed{\boxed{\tt{Length \: \: of \: \: Triangular \: \: field \: \: to \: \: be \: \: \: fenced = \: \bf{260 \: m}}}}}$

~ For total cost of Double Fencing the field :-

$\large{\longrightarrow \: \: \: \: \sf{Total \: cost \: of \: fencing \: = \: \bf{Perimeter \: of \: field \: to \: fenced \: \times \: Rate \: of \: fencing}}}$

➣ Total Cost of Double Fencing = 460 m × 6 per m

➣ Total cost of double fencing = ₹ 2,760

$\: \\ \large{\boxed{\boxed{\tt{Total \: \: cost \: \: of \: \: fencing \: \: Triangular \: \: field \: \: = \: \bf{Rs. \: 2,760}}}}}$

$\: \large{\rm{\longmapsto \: \: \underline{\underline{Hence, \: total \: cost \: of \: double \: fencing \: triangular \: field_{(\Delta)} \: is \: \: \boxed{\bf{Rs. \: 2,760}}}}}}$

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$\: \: \large{\sf{\underbrace{Aid \; to \; Memory} \: :-}}$

• Area of Square = (Side)²

• Area of Rectangle = Length × Breadth

• Area of Parallelogram = Height × Base

• Area of Triangle = ½ × Base × Height

Answer 2

Given,

A gardener has to put double fence all around the triangular field of side 120m, 80m and 60m . In the middle of each side there is a gate of width 10 m.

To find :

Find the rate of fencing at the rate of Rs. 6/m.

Solution :

Sides of triangular field = 120m, 80m and 60 m

∴ Perimeter of triangular field = 120 + 80 + 60

∴ Perimeter of triangular field = 260 m

Now, given that width of each gate = 10m , so finding total length of wire needed for double fence :

⇒  Length of wire needed = 2 * {Perimeter of field - - 3(10)}

⇒  Length of wire needed = 2 * {260 - 30}

⇒  Length of wire needed = 2 * 230

⇒  Length of wire needed = 460 m

Now we know,

⇒  Rate of fencing = Length of wire * Rate

⇒  Rate of fencing = 460 * 6

⇒  Rate of fencing = Rs. 2760

Therefore,

Rate of double fencing = Rs. 2760