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?



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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.

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

Areaofrectangle=length×breadth[/tex]

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

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

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

2

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

45

14580

=x

2

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

2

$sf \longrightarrow x = \sqrt{324}⟶x= </p><p>324$

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

x=18

⋆

We have taken,

Length = 9x = 9×18 = 162 m

Breadth = 5x = 5×18 = 90 m.

Answer 2

Answer:

Let the length of rectangle be 9x and its breadth be 5x

So,

Area = l × b

⇒ 14580 = 9x × 5x

45x2 = 14580

x2 = 14580/45 = 324

x = √324

x = 18

Hence,

Length = 9 × 18 = 162 m and Breadth = 5 × 18 = 90 m

Now, Perimeter = 2(l + b)

= 2 (162 + 90) = 2(252)

= 504 m.

Therefore, cost for fencing the surrounding 504 m at the rate of ₹3.25 per metre = ₹(504 × 3.25) = ₹1638

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