Question

The length and breadth of a rectangular field are in the ratio 9 : 5. If the area of the field is 14580 square metre, find the cost of surrounding the field with a fence at the rate of Rupees 3.25 per metre?​

Answer 1

Given:-

• Length and breadth of rectangular field are in ratio 9:5.
• Area of field is 14580 m sq.

To find:-

• Cost of fencing the surrounding of field.

Solution:-

Let, Length of rectangular field be 9x.

And Breadth of rectangular field be 5x.

$\boxed{ \sf \bold{Area \: of \: rectangle = length \times breadth}}$

Put area, length and breadth of rectangular field in formula:

$\sf \longrightarrow 14580 = 9x \times 5x$

$\sf \longrightarrow 14580 = 45 {x}^{2}$

$\sf \longrightarrow \dfrac{14580}{45} = {x}^{2}$

$\sf \longrightarrow 324 = {x}^{2}$

$\sf \longrightarrow x = \sqrt{324}$

$\sf \longrightarrow \green{ \boxed{ \sf \bold{x = 18}} \star}$

We have taken,

Length = 9x = 9×18 = 162 m

Breadth = 5x = 5×18 = 90 m.

$\boxed{ \sf \bold{Perimeter\: of \: rectangle = 2(length + breadth)}}$

Put length and breadth,

$\sf \longrightarrow 2 \times (162 + 90)$

$\sf \longrightarrow 324 + 180$

$\sf \longrightarrow \red{ \boxed{ \sf \bold{504}} \star}$

Perimeter of rectangular field is 504 m.

• We know fence and perimeter are same.

So, Fence of rectangular field is 504 m.

1 m = Rs 3.25

For 504 m -

$\sf \longrightarrow 504 \times 3.25$

$\sf \longrightarrow \purple{ \boxed{ \sf \bold{1638}} \bigstar}$

Therefore,

Cost for fencing rectangular field is Rs. 1638 .

Answer 2

Answer:

$\huge \bf \: Given$

• Length and breadth of a rectangular field = 9:5
• Area of field = 14580 m²
• Cost of fence per metre = ₹3.25

$\huge \bf \: To \: find \:$

Total cost

$\huge \bf \: Solution$

Let the length be 9x and Breadth be 5x

$\sf \implies \: 14580 = 9x \times 5x$

$\sf \implies \: 14580 = 45 {x}^{2}$

$\sf \implies \: \dfrac{14580}{45} = {x}^{2}$

$\sf \implies \: 324 = {x}^{2}$

$\sf \implies \: x \: = \sqrt{} 324$

$\small \bf \: x \: = 18$

Now,

Finding length and breadth

$\sf \: 9x = 9(18) = 162$

$\sf 5x = 5(18) = 90$

Now,

Finding perimeter

$\fbox {Perimeter \: = 2(l + b)}$

$\sf \implies \: Perimeter \: = 2(162 + 90)$

$\sf \implies Perimeter \: = 2(252)$

$\fbox {Perimeter = 504 \: m}$

Now,

Finding total cost

$\sf \: Cost \: of \: fence \: 1 \: m= 3.25$

$\sf \: Cost \: of \: fence \: 504 \: m \: = 1638$