Question

Solve the following:
1. The length and breadth of a rectangular field are in the ratio 3:2. If the area of the field is 3456 m2 , find the cost of fencing the field at Rs 3.50 per metre.​

Answer 1

Answer:

Let the sides be 2x and 3x

2x × 3x = 3456

6x sq = 3456

x sq = 576

x = 24

Length = 2×24 = 48

Breadth = 3×24 = 72

Cost of fencing = Perimeter × Rate

Perimeter = 2(48+72) = 240

240 ×3.50 = 840

Answer 2

$\Large{\underline{\underline{\red{\sf{AnsWer :}}}}}$

Cost of fencing = Rs 840

$\large{\underline{\underline{\red{\sf{Step-By-Step-Explanation :}}}}}$

The ratio of length and breadth is 3:2

So,

length = 3x

breadth = 2x

And Area is 3456 cm²

For finding Area of rectangle we have formula :

$\Large{\boxed{\boxed{\blue{\sf{\star \: Area \: = \: l \: \times \: b}}}}}$

Put Values

$\rightarrow{ \sf{3465 \: = \: 3x \: \times \: 2x}}$

$\rightarrow {\sf{3465 \: = \: 6x^2}}$

$\displaystyle \rightarrow {\sf{x^2 \: = \: \frac{\cancel{3465}}{\cancel{6}}}}$

$\rightarrow {\sf{x \: = \: \sqrt{576}}}$

$\rightarrow {\sf{x \: = \: 24}}$

Length = 3(24)

⇒ Length = 72

Bredth = 2(24)

⇒Breadth = 48

$\rule{200}{2}$

Formula for perimeter of rectangle is :

$\Large{\boxed{\boxed{\blue{\sf{Perimeter \: = \: 2(l \: + \: b)}}}}}$

⇒ Perimeter = 2(48 + 72)

⇒Perimeter = 2(120)

⇒Perimeter = 240

Cost of Fencing

⇒ Perimeter * 3.50

⇒Cost = 240 * 3.50

$\Large{\boxed{\boxed{\sf{Cost \: = \: Rs \: 840}}}}$