Question

L-14. Perimeter and Area -II
The length and breadth of a rectangular field are in the ratio 3 : 2. If the area of the field is 3456 m², find
the cost of fencing it at Rs. 60 per m.
321271 ? -
Find the area of a rect​

Answer 1

Answer:

The cost of fencing the rectangular field is ₹11,520

Step-by-step explanation:

Given that, Length and breadth of a rectangle are in the ratio 3 : 2 respectively. The area is 3456m².

Here, the dimensions are ratio and the area is given. So, we need to find it's cost of fencing at ₹60 per metres.

Step 1 : Let's assume the dimensions of the field :

➪ Length = $3x$

➪ Breadth = $2x$

Step 2 : Calculate the value of $x$ :

We know that,

Area of a rectangle = $l \times b$

But, area of the rectangle is 3456m² (given)

${ \underline{ \boldsymbol{According \: to \: the \: question : }}}$

$\implies 2x \times 3x = 3456$

$\implies {6x}^{2} = 3456$

$\implies {x}^{2} = \dfrac{3456}{6}$

$\implies {x}^{2} = 576$

$\implies x = \sqrt{576}$

${\therefore { \boldsymbol{The \: value \: of \: x = 24}}}$

Step 3 : Calculate their dimensions :

➪ Length = $3x = 3(24) = \bf 72m$

➪ Breadth = $2x = 2(24) = \bf 48m$

Step 4 : Find the length of fencing :

• The fencing is the perimeter of the rectangular field.

Perimeter of a rectangle is given by : $2(l + b)$

Where,

• $l$ (length) = 72m.
• $b$ (breadth) = 24m.

So, perimeter of the rectangle is :

→ 2(72 + 24)

→ 2(96)

→ 192metres.

Step 5 : Calculate the cost of fencing :

Cost of fencing is given by :

perimeter of the rectangle × rate of fencing

• Rate of fencing is ₹60 per metres. (given)

So, the cost of fencing the rectangle is :

→ ₹60 × 192

→ ₹11,520