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.

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

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

Required Answer:-

Given:

1. The length and breadth of a field are in the ratio 9:5.
2. Area of the field is 14580m²

To find:

• Cost of surrounding the field @₹3.25 per metre.

Answer:

• The total cost of surrounding the field is ₹1638.00/-

Solution:

Let the length of the field be 9x.

Let the breadth of the field be 5x.

We know that,

Area of a rectangle = Length × Breadth

Here,

Area of the rectangular field = 14580m²

Length = 9x m

Breadth = 5x m

According to the given conditions,

➡ 9x × 5x = 14580

➡ 45x² = 14580

➡ x² = 14580/45

➡ x² = 324

➡ x = √324

➡ x = ±18

But, length of side cannot be negative.

So,

x = 18m.

Hence,

Length = 9x = 9 × 18 = 162m.

Breadth = 5x = 5 × 18 = 90m.

Perimeter of the rectangular field

= 2 × (Length + Breadth)

= 2 × (162 + 90)m

= 2 × 252

= 504m

So, total cost of surrounding the field @₹3.25/m is,

= ₹3.25 × 504

= ₹1638

Hence, total cost of surrounding the field is ₹1638.09/- (Answer)