Question

The cost of levelling a rectangular garden at rupees 3.50 square metre is 8400 its length and breadth are in the ratio 3 ratio 2 find the perimeter of the garden

Answer 1

Answer:

Perimeter of the rectangular garden is 200.0 m.

Step-by-step explanation:

= > Cost of levelling = area to be levelled x rate of levelling

= > ₹8400 = area to be levelled x ₹3.50 / m^2

= > ( ₹8400 ) / ( ₹3.50 ) m^2 = area to be levelled

= > 2400.00 m^2 = area to be levelled

Since the whole rectangular garden is to be levelled, area to be levelled = area of rectangular garden = 2400.00 m^2

Given,

Length : Breadth = 3 : 2

= > Length = ( 3 / 2 ) breadth

From the properties of rectangular structures( 2D ) :

• Area of rectangle = length x breadth
• Perimeter of rectangle ( 2D ) = 2( length + breadth )

Here,

= > Area of rectangular garden = 2400.00 m^2

= > length x breadth = 2400.00 m^2

= > ( 3 / 2 ) x breadth x breadth = 2400.00 m^2

= > breadth^2 = 2 x 2400.00 / 3 m^2

= > breadth^2 = 1600.00 m^2

= > breadth = 40.0 m

Thus, length = 3 / 2 x 40.0 m = 60 m

Therefore : Perimeter of rectangular garden = 2( 60.0 m + 40.0 m ) = 2( 100.0 ) = 200.0 m

Hence perimeter of the rectangular garden is 200.0 m.

Answer 2

$\huge{\underline{\underline{\mathbb{\pink{Solution}}}}}$

$\underline\mathbb \green{given}$

Cost of leveling per sq m = Rs 3.5

Total cost of leveling garden = Rs 8400

Ratio of length and breadth = 3 : 2

$\mathbb \pink{to \: find \: area \: of \: garden \: divide \: total \: cost \: with \: cost \: per \: sq \: m}$

$area \: = \frac{8400}{3.5}$

area = 2400 m²

$\mathbb \green{area \: of \: rectangle \: = l \times b}$

2400 = 3x × 2x

2400 = 6x²

$\frac{2400}{6} = {x}^{2}$

400 = x²

x = 20 m

Now length of rectangular garden = 3(20) = 60 m

Breadth of rectangular garden = 2(20) = 40 m .

$\mathbb \pink{perimeter \: = 2(l + b)}$

Perimeter = 2 ( 60 + 40 )

Perimeter = 200 m

So the perimeter of given rectangular garden is 200 m .