Question

please answer the question with full solution ​

Answer 1

Given:

• Length of a rectangle field is ${\green{\bf{thrice\: it's \:breadth}}}$

• area of the rectangle is $\bf\blue{7500m²}$

• Cost to fence it per meter is $\bf\pink{Rs.10}$

To Find:

• the total cost of fencing the field

Solution:

❍ here, as it's said the we have to find the total cost of fencing so first we have to find the perimeter of the rectangle and then multiply it with the cost per meter

Now, let's find the dimensions of the rectangle

Assume,

• ➪ Length as $\bf{\pink{ 3X}}$
• ➪ Breadth as $\bf{\blue{ X}}$

$\purple{ \underline{ \mathfrak{As \: we \: know \: that \dag}}}$

${ \longrightarrow}\blue{ \underline{ \boxed{ \pink{ \mathfrak{ area \: of \: a \: rectangle =l \times b}}}} \bigstar}$

Where,

• L stands for length
• B stands for breadth

Let's substitute the values and find the dimensions:

$\longrightarrow \sf \: lenght \times breadth = 7500 {m}^{2} \\ \\ \\ \longrightarrow \sf \: 3x \times x = 7500 {m}^{2} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \longrightarrow \sf \: 3 {x}^{2} = 7500 {m}^{2} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \longrightarrow \sf \: {x}^{2} = \cancel\frac{7500}{3} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \longrightarrow \sf \: {x}^{2} = 2500 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \longrightarrow \sf \: x = \sqrt{2500} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \orange{\longrightarrow \sf \: x = 50 \bigstar} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

hence ,

• Length = ${\bf{\gray{3X = 150m}}}$
• Breath = ${\bf{\gray{X = 50m}}}$

As we have found the length and breadth let's find the perimeter now,

$\purple{ \underline{ \mathfrak{As \: we \: know \: that \dag}}}$

${\longrightarrow}\blue{ \underline{ \boxed{ \pink{ \mathfrak{ \: perimeter \: of \: a \: rectangle = 2(l + b) }}}} \bigstar}$

Where,

• L stands for length
• B stands for breadth

Let's substitute the values again to find the perimeter:

${ : \implies} \tt \: perimeter \: = 2(150 + 50) \\ \\ \\ { : \implies} \tt \: perimeter = 2(200) \: \: \: \: \: \: \: \: \: \: \\ \\ \\ { : \implies} \tt \: perimeter \: = 400m \: \: \: \: \: \: \: \: \: \: \:$

$\rm{ \underline{ \therefore \: perimeter \: of \: the \: field \: = 400m}}$

Now, let's find the cost of fencing:

• Cøst of fencing per meter is rs.50

$\dashrightarrow \sf \: cost \: to \: fence \: = 400 \times 50 \: \: \: \: \: \\ \\ \\ \dashrightarrow \bf \: cost \: to \: fence \: = rs.20000$

➪ hence the cost to fence the field is 2,0000

▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬

More to know:

• Area of Square = Side x Side
• Area of Rectangle = Length × Breadth
• Area of Triangle = ½ × base x height
• Area of parallelogram = base x height
• Area of circle = πr²
• Area of Rhombus = ½ × product of its diagonals
• Area of Trapezium = ½ × height × sum of parallel sides
• Area of Polygon = sum of the area of all regions into which it is divided

hope this helps.!