Question

The length and breadth of a rectangular field are in the ratio 2:3. If the area of the field is 3456m sq.,find the cost of fencing the field at rs 3.50 per m

Answer 1

lgth=2X brth=3X
area=6X square=3456
X square=3456/6
X square=576
X=24
l=48 b=72
2 (l+b)=2×120=240
240×3.5=840

Answer 2

Let the length of the field be 2x m

Then , it's breadth = 3x m.

So , Area of the field =( Length × Breadth ) sq. unit

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀= ( 2x × 3x)m²

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀= ( 6x²) m²

But , area = 3456m² ( given )

So, 6x² = 3456 =》x² =

$\frac{3456}{6} = 576$

x =

$\sqrt{576 } = 24.$

So, Length = ( 2 × 24 ) m

⠀⠀⠀⠀⠀⠀⠀= 48 m

⠀⠀ Breadth = ( 3 × 24 )m

⠀⠀⠀⠀⠀⠀⠀⠀= 72 .

Then , Perimeter of field = 2( l + b)

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀= 2 ( 72 + 48 )m

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀= ( 2 × 120 )m

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀= 240 m .

Hence , the cost of fencing = Rs. ( 240 × 3.50 )

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀= Rs. 840 ans.

$\huge\mathcal\color{teal}Hope\:it\:helps!!$