Question

$\huge\sf\color{purple}{\underline{\underline{\underline{Question}}}$

the length and the breadth of a rectangular field are in the ratio 3:2 . If the area of the field is 3456 m² .find the cost of fencing it at rupees 60 per metre.​

Answer 1

Answer:

$\huge\color{pink}{ \colorbox{black}{\colorbox{white}{Solution:}}}$

$\rm{Length \: of \: a \: rectangle \: field =3x}$

$\rm{Breadth \: of \: a \: rectangle \: field =2x}$

$\rm{Area =3456 m^{2} }$

$\rm{3x \: × \: 2x=3456 m^{2} }$

$\rm{6x^{2} =3456 m ^{2} }$

$\rm{x^{2} =576 m^{2} }$

$\rm{x=24 m}$

$\rm{∴ \: Length=72m}$

$\rm{Breadth =48 m}$

$\rm{Perimeter \: of \: the \: rectangular \: field =72+48=120m}</p><p>$

$\rm{Cost \: of  \: 1 m =Rs.60}$

$\rm{Cost \: of \:  120  \: m=Rs. \: 60 \times 120 = Rs.7200}$

Step-by-step explanation:

Hope it helps you!

Answer 2

Given:

• Area of a rectangular field = 3456 m²
• The length and breadth of a rectangular field are the ratio 3 : 2
• Rate of Fencing = Rs. 60 per meter.

To Find:

• The total money required to Fence the ground.

Formula used:

$\\ \bigstar{\underline{\boxed {\bold{ \color{red}{Area \: \: of \: \: rectangle = Length × Breadth}}}}}$

$\bigstar{\underline{\boxed {\bold{ \color{blue}{perimeter \: \: of \: \: rectangle = 2(Length + Breadth)}}}}}$

Solution:

Let ,

• the length of rectangular field be 3x
• breadth of the rectangular field be 2x .

☆ Calculating the length and Breadth of rectangular field ;

$\\ \sf\dashrightarrow \: \: 3 \: x \: × \: 2 \: x \: = \: 3456$

$\sf\dashrightarrow \: \: 6 \: \: x \: ² = \: 3456$

$\sf\dashrightarrow \: \: x \: ² = \frac{3456}{6}$

$\sf\dashrightarrow \: \: x \: ² = \: 576$

$\sf\dashrightarrow \: \: x \: ² = \: ( \: 24 \: ) \: ²$

$\sf\dashrightarrow \: \: x \: = \: ( \: 24 \: ) \:$

Therefore:

• Length = 3x = 3 × 24 = 72 m
• Breadth = 2x = 2 × 24 = 48 m

☆ calculating the perimeter of rectangular field:

$\\ \sf\dashrightarrow \: \: 2 \: (L \: + \: B )\:$

$\\ \sf\dashrightarrow \: \: 2 \: (72 \: + \: 48 )\:$

$\\ \sf\dashrightarrow \: \: 2 \: \times \: 120\:$

$\\ \sf\dashrightarrow \: \: 240 \: \: m\:$

☆ Calculating the cost of fencing the field at Rs 60 per metre:

➪ Cost of fencing 1 m = Rs 4.50

➪ Cost of fencing 240 m = Rs 60 × 240

➪ Cost of fencing 240 m = Rs 14,400