Question

L:B =9:5 . Area is 14580 m square. Find the cost of fencing the field@ rupees 4.25/ m
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Answer 1

Appropriate Question:

Length and breadth of a rectangular field is in the ratio of 9:5. Area is 14580 m² .Find the cost of fencing the field at a rate of Rs 4.25 per m.

Required Solution:

★ Rs 2142 ★

Given:

• Length and breadth are in the ratio of 9:5.

• Area of the field = 14580 m²

• Cost of fencing per m² = Rs 4.25

To calculate:

• Cost of fencing the field.

Calculation:

As we have to find the cost of fencing the field, so we need to calculate the perimeter of the field first.

In order to calculate the perimeter of field, we also have to calculate the length and breadth of the field.

→ Let us assume the length and breadth of the rectangular field as 9x and 5x.

Calculating length and breadth:

We know that,

• Area of rectangle = length × breadth

According to the question:–

→ 14580 = 9x × 5x

→ 14580 = 45x²

→ 14580/45 = x²

→ 324 = x²

→ √324 = x

→ 18 = x

Therefore,

• Length = 9x

⇒ Length = ( 9 × 18 )m

⇒ Length = 162 m

• Breadth = 5x

⇒ Breadth = ( 5 × 18 )m

⇒ Breadth = 90 m

Now,

• Perimeter of the rectanglular field = 2 ( l + b )

→ Perimeter of the rectangular field = 2 ( 162 + 90 )

→ Perimeter of the rectangular field = 2 ( 252 )

→ Perimeter of the rectangular field = 504 m

Therefore, cost of fencing the field :–

→ Rs ( 4.25 × 504 )

→ Rs 2142

Answer 2

${\underline{\underline{\bf{Given:}}}}$

• Area of a rectangular field is 14,580 m².
• Its length and breadth are in the ratio of 9 : 5.
• The cost of fencing the field per m² is 4.25/-

${\underline{\underline{\bf{Need\:to\:find:}}}}$

• The cost of fencing the field.

${\underline{\underline{\bf{Formulae\:to\:be\:used:}}}}$

$\underline{\boxed{\sf{{Area}_{[Rectangle]}=lb\:sq.units}}}$

$\underline{\boxed{\sf{{Perimeter}_{[Rectangle]}=2(l+b)\:units}}}$

${\underline{\underline{\bf{Solution:}}}}$

We've to find the cost of fencing the field. For that, the measure of perimeter of the field is necessary. Here, we're given with the area of the field and it is said that the length and breadth are in a ratio. Since, the we don't know the measure of length and breadth, we cannot find the perimeter. So, first let's find the length and breadth of the field.

Length and breadth of the field:

Let,

The measure of length be 9x

And the measure of breadth be 5x

Now, we can find the value of x by substituting the expressions in place of length and breadth in the formula of area of rectangle.

$\:\:\:\:\:\:\:\implies{\sf{{Area}_{[Rectangle]}=lb\:sq.units}}$

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

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

$\:\:\:\:\:\:\:\implies{\sf{\Large{\frac{\cancel{14850}}{\cancel{45}}}=x^2}}$

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

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

$\:\:\:\:\:\:\:\implies\underline{\sf{18=x}}$

Now, we know the value of 'x'. So, we can substitute it in its place in the expressions formed for length and breadth.

• Length$\rightarrow{\sf{9x=9\times 18={\underline{\underline{162\:m}}}}}$
• Breadth$\rightarrow{\sf{5x=5\times 18={\underline{\underline{90\:m}}}}}$

We've obtained the measures of length and breadth of the field. Now, we can find the perimeter.

$\:\:\:\:\:\:\:\implies{\sf{P=2(l+b)\:units}}$

By substituting the measures,

$\:\:\:\:\:\:\:\implies{\sf{P=2\times (162+90)}}$

$\:\:\:\:\:\:\:\implies{\sf{P=2\times 252}}$

$\:\:\:\:\:\:\:\implies{\underline{\underline{\sf{{Perimeter}_{[Rectangle]}=504\:m}}}}$

★ Cost of fencing the field:

$\rightarrow{\sf{Perimeter\:of\:field\times Cost\:per\:{m}^{2}}}$

By substituting the values,

$\rightarrow{\sf{504\times 4.25}}$

$\rightarrow{\sf{\red{\underline{\underline{2142/-}}}}}$

${\underline{\underline{\bf{Required\: answer:}}}}$

• 2142/- is required to fence the rectangular field.

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