Question

The sides of a rectangular pack are in the ratio 4:3 . If it's area is 1728 m^2 . Find the cost of fencing in at 30 rs/m​

Answer 1

Question:-

The sides of a rectangular pack are in the ratio 4:3 . If it's area is 1728 m² . Find the cost of fencing in at 30 rs/m.

Answer:-

• The cost of fencing is ₹5,040.

To find:-

• Cost of fencing

Solution:-

Put x in ratio

sides are:-

1. 4x
2. 3x

• Area = 1728 m²

$\boxed{ \large{area = length \times breadth}}$

$\implies \: 4x \times 3x = 1728 \\ \\ \implies \:12 {x}^{2} = 1728 \\ \\ \implies \: {x}^{2} = \frac{1728}{12} \\ \\ \implies \: {x}^{2} = 144 \\ \\ \implies \:x = \sqrt{144 } \\ \\ \implies \:x = 12$

• Length= 4x = 4×12 = 48 m
• Breadth = 3x = 3× 12 = 36 m

$\boxed { \large{perimeter = 2(length + breadth}}$

$\implies \: perimeter = 2(48 + 36) \\ \\ \implies \: perimeter =2 \times 84 \\ \\ \implies \: perimeter =168 \: m$

• The perimeter of rectangle is 168 m.
• Cost of fencing (per m²) =₹30

$\implies \: total \: cost =30 \times 168 \\ \\ \implies \: total \: cost = 5,040$

• The cost of fencing is ₹5,040.

Answer 2

$\huge\mathbf\red{Question :-}$

The sides of a rectangular pack are in the ratio 4:3 . If it's area is 1728 m^2 . Find the cost of fencing in at 30 rs/m

$\huge\mathbf\pink{To\: Find :- }$

• Cost of Fencing

$\huge\mathbf\purple{Solution:-}$

• Let the sides of the park be 4x and 3x.

Area of the park = 1728

Length × breadth = 1728

4x × 3x = 1728

12x² = 1728

= 1728x² = 1728/12

x = $\sqrt{144}$

x = 12

Therefore,

Length & breadth = 2×2×3 = 12

Hence,

• Length = 4×12=48
• Breadth = 3×12=36

Perimeter = 2(48+36)

Perimeter = 2(48+36)= 2×84= 168 m

• Cost of fencing = ₹(168×30)

$\huge\mathbf\green{= ₹5,040}$