Question

The cost of levelling a rectangular garden at rupees 3.50 per sq m. is rs 8400 . Its length and breadth are in the ratio 3:2. Find the perimeter of the garden?​

Answer 1

Given :

• Cost of levelling the rectangular garden = Rs 8400

• Cost of garden per m² = Rs. 3.50

• Ratio of length is to breadth = 3 : 2

To find :

The Perimeter of the garden.

Solution :

According to the given information , the total cost and the cost per m² , but we know that :

Total cost of levelling the garden = Area of the garden × cost of levelling per m²

Let the area of the garden be x m².

Now , using the above concept and substituting the values in it, we get :

$:\implies \bf{8400 = x \times 3.50}$

$:\implies \bf{\dfrac{8400}{3.50} = x}$

$:\implies \bf{\dfrac{840000}{350} = x}$

$:\implies \bf{2400 = x}$

$\boxed{\therefore \bf{Area\:(A) = 2400\:m^{2}}}$

Hence, the area of the field is 2400 m².

To find the sides of the Rectangle :

Let the length be 3x and the breadth be 2x.

Now, using the formula for area of a Rectangle and substituting the values in it, we get :

$:\implies \bf{Area = Length \times Breadth}$

$:\implies \bf{2400 = 3x \times 2x}$

$:\implies \bf{2400 = 6x^{2}}$

$:\implies \bf{\dfrac{2400}{6} = x^{2}}$

$:\implies \bf{400 = x^{2}}$

$:\implies \bf{\sqrt{400} = x}$

$:\implies \bf{20 = x}$

$\boxed{\therefore \bf{x = 20\:m}}$

Hence, the value of x is 20 m.

Now , putting the value of x in the length and breadth of the Rectangle , we get :

• $:\implies \bf{Length = 3x}$

$:\implies \bf{L = 3 \times 20}$

$:\implies \bf{L = 60}$

$\boxed{\therefore \bf{L = 60}}$

Hence, the length of the Rectangle is 60 m.

$:\implies \bf{Breadth = 2x}$

$:\implies \bf{B = 2 \times 20}$

$:\implies \bf{B = 40}$

$\boxed{\therefore \bf{B = 40}}$

Hence, the breadth of the Rectangle is 40 m.

Perimeter of the Rectangle :

Using the formula for and substituting the values in it, we get :

$:\implies \bf{Perimeter = 2(length + breadth)}$

$:\implies \bf{P = 2(60 + 40)}$

$:\implies \bf{P = 2 \times 100}$

$:\implies \bf{P = 200}$

$\boxed{\therefore \bf{Perimeter = 200}}$

Hence, the perimeter of the Rectangle is 200m.

Answer 2

Given:

★ Length and Breadth are in the Ratio 3:2

★ Cost of levelling a Rectangular garden at rs. 3.50/m² is rs. 8400

Find:

★ The Perimeter of Garden

Solution:

Let,

$\sf \star \red{Length \: of \: rectangle = 3x}$

$\sf \star \blue{Breadth \: of \: rectangle = 2x}$

$\to \sf \pink{Area \: of \: rectangle = l \times b}$

$\to \sf \pink{Area \: of \: rectangle = 3x \times 2x}$

$\to \sf \pink{Area \: of \: rectangle = 6 {x}^{2} }$

____________________

$\footnotesize{\hookrightarrow \purple{\sf Cost \: of \: levelling = area \: of \: rectangle \times 3.50}}$

$\footnotesize{\hookrightarrow \purple{\sf 8400= 6 {x}^{2} \times 3.50}}$

$\footnotesize{\hookrightarrow \purple{\sf 8400= 6 \times {x}^{2} \times 3.50}}$

$\footnotesize{\hookrightarrow \purple{\sf 8400= 6 \times 3.50 \times {x}^{2} }}$

$\footnotesize{\hookrightarrow \purple{\sf 8400= 21\times {x}^{2} }}$

$\footnotesize{\hookrightarrow \purple{\sf \cancel{\dfrac{8400}{21}} = {x}^{2} }}$

$\footnotesize{\hookrightarrow \purple{\sf {x}^{2} = 400}}$

$\footnotesize{\hookrightarrow \purple{\sf x= \sqrt{400} }}$

$\footnotesize{\hookrightarrow \purple{\sf x= 20m}}$

____________________

$\sf \therefore length = 3x = 3 \times 20 = 60m$

$\sf and \: breadth = 2x = 2\times 20 = 40m$

$\sf \to \orange{ Perimeter = 2(l + b)}$

$\sf \to \orange{ Perimeter = 2(60 + 40)}$

$\sf \to \orange{ Perimeter = 2(100)}$

$\sf \to \orange{ Perimeter = 200m}$

$\small{\underline{ \sf\therefore perimeter \: of \: rectangle \: is \: 200m}}$