Question

The sides of rectangular park are in the ratio 4.3 .if the area is 172
8 m²,find the cost of fencing it at the rate of Rs. 2.50/m ?

Answer 1

AnswEr :

• Sides of Rectangluar Park = 4 : 3
• Area of Park = 1728 m²
• Rate of Fencing = Rs. 2.50 @metre
• Find the Cost of Fencing.

Let the Sides be 4n, and 3n of Park.

⋆ Refrence of Image is in the Diagram :

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• According to the Question Now :

$\longrightarrow \tt Area \:of \:Park = Length \times Breadth \\ \\\longrightarrow \tt1728 = 4n \times 3n \\ \\\longrightarrow \tt1728 = 12 {n}^{2} \\ \\\longrightarrow \tt \cancel \dfrac{1728}{12}={n}^{2} \\ \\ \longrightarrow \tt144 = {n}^{2} \\ \\\longrightarrow \tt \sqrt{144} = n \\ \\\longrightarrow \tt \sqrt{12 \times 12} = n \\ \\\longrightarrow \tt n = 12$

$\rule{300}{1}$

• D I M E N S I O N S :

◗ Length = 4n = 4(12) = 48 m

◗ Breadth = 3n = 3(12) = 36 m

$\rule{300}{2}$

• Cost of Fencing of Rectangluar Park :

$\implies \tt Total\:Cost = Perimeter \times Rate \\ \\\implies \tt Total\:Cost = 2(Length+ Breadth) \times Rate \\ \\\implies \tt Total\:Cost = 2(48 + 36) \times 2.50 \\ \\\implies \tt Total\:Cost = \cancel2 \times 84 \times \dfrac{5}{ \cancel2}\\ \\\implies \tt Total\:Cost =84 \times 5 \\ \\ \implies \boxed{\blue{\tt Total\:Cost =Rs. \:420}}$

⠀

∴ Total Cost of Fencing of Park is Rs.420

#answerwithquality #BAL

Answer 2

$\bf{\Huge{\underline{\boxed{\sf{\green{ANSWER\::}}}}}}$

$\bf{\Large{\underline{\bf{Given\::}}}}$

The sides of rectangular park are in the ratio 4:3.If the area is 1728m².

$\bf{\Large{\underline{\bf{To\:find\::}}}}$

Th cost of fencing it at the rate of Rs.2.50/m².

$\bf{\Large{\underline{\boxed{\sf{\blue{Explanation\::}}}}}}$

Let the ratio be R.

$\bf{We\:have\begin{cases}\sf{The\:length\:of\:rectangular\:park=4R}\\ \sf{The\:breadth\:of\:rectangular\:park=3R}\\ \sf{The \:area\:of\:rectangular\:park=1728m^{2}} \end{cases}}$

We know that area of rectangle: $\sf{\red{(Length*Breadth)}}$

→ 4R × 3R = 1728m²

→ 12R² = 1728m²

→ R² = $\bf{\cancel{\frac{1728}{12} m^{2} }}$

→ R² = 144m²

→ R = √144m²

→ R = 12m

Therefore,

• The length of the rectangular park = 4(12) = 48m.
• The breadth of the rectangular park = 3(12) = 36m.

&

We know that perimeter of rectangle: $\sf{\red{2(Length+breadth)}}$

⇒ 2(48 + 36)m

⇒ 2(84)m

⇒ 168m

Now,

→ The cost of fencing at the rate of Rs.2.50 per m².

→ The cost of fencing 168m at the rate = Rs.(2.50×168)

→ The cost of fencing 168 at the rate = Rs.420.