Question

The length and breadth of a rectangular field are in the ratio of 3:2 if the area of the field is 3456 sq m find the cost of fencing the field at rupees 4 per meter

Answer 1

let length be 3x and breadth be 2x
area is given 3456 m²
acc. to question
3x × 2x = 3456m²
6x² = 3456 m²
x² = 3456 m²/6
x =√576m²
x = 24 m

now lenght is 3x =72
and breadth 2x = 48

now fencing at the cost 4 rs per metremeans perimeter i.e 2(l+b) ×4 rs
2(72+48)×4
2(120) × 4
240 ×4
960


therefore,
total cost for fencing the field is Rs.960

Answer 2

$\huge{\underline{ \underline {\sf {\blue{Required \: Answer}}}}}$

Given:-

• Length and breadth of a rectangular field is in the ratio of 3:2
• Area of field is 3456 m²

To Find:-

• Cost of fencing the field at the rate of Rs.4 per metre.

$\huge {\underline{ \underline {\fcolorbox{red}{purple}{Solution}}}}$

Firstly we'll find length and breadth of of field.

⟼ Let Length be = 3x

⟼ Let breadth be = 2x

Using Formula :

${ \fbox \red{Area \: of \: rectangle = l × b}}$

Putting Values :

$⟼ \: 3456 = 3x \times 2x \\ ⟼ \: \: \: \: \: \: \: \: 3456 = {6x}^{2} \\ ⟼ \: \: \: \: \: \: \: \: \: \frac{3456}{6} = {x}^{2} \\ ⟼ \: \: \: \: \: \: \: \: \: \: \: \sqrt{576} = x \\ ⟼ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: 24 = x$

Value of x is 24

Therefore,

⟼ Length of field = 3(24)

⟼ 72 m

⟼ Breadth of field = 2(24)

⟼ 48

Now;

⟼ Length = 72 m

⟼ Breadth = 48 m

Using Formula :

${ \underline{ \underline {\fcolorbox{red}{blue}{Perimeter \: of \: rectangle = 2(l + b)}}}}$

Putting Values :

⟼ 2(72 + 48)

⟼ 2(120)

⟼ 240 m

Cost of fencing the field at the rate of Rs. 4 per m.

⟼ 240×4

⟼ Rs.960

• The cost of fencing the field at rupees 4 per meter is Rs.960