ESSAY TYPE QU12. The ratio of the length and breadth of a 16rectangula

1.	ESSAY TYPE QU12. The ratio of the length and breadth of a 16rectangular field is 3:2 and its area is 11094sq m. What will be the cost of fencing thefield at the rate of 2.50 per metre?
Answer» ✬ Cost = Rs 1075 ✬ Step-by-step explanation: Given: Ratio of length and breadth of rectangular field is 3 : 2. Area of field is 11094 m². Cost of fencing is Rs 2.50 per meter. To FIND: What will be the cost of fencing whole rectangular field ? Solution: Let x be the common in given ratio. Therefore, Length = 3x & Breadth = 2x We know that the ★ Area of Rectangle = ( Length $\times$ Breadth ) sq units ★ But A/q Area = 11094 m² $\implies{\rm }$ 11094 = ( Length $\times$ Breadth ) $\implies{\rm }$ 11094 = ( 3x $\times$ 2x ) $\implies{\rm }$ 11094 = 6x² $\implies{\rm }$ 11094/6 = x² $\implies{\rm }$ 1849 = x² $\implies{\rm }$ √1849 = x $\implies{\rm }$ √43 $\times$ 43 = x $\implies{\rm }$ 43 m = x So, ➟ Length = 3x = 3 $\times$ 43 = 129 m ➟ Breadth = 2x = 2 $\times$ 43 = 86 m Since, fencing will be done in perimeter of rectangular field. ★ Perimeter = 2 ( Length + Breadth ) ★ $\implies{\rm }$ 2 ( 129 + 86 ) $\implies{\rm }$ 2 $\times$ 215 $\implies{\rm }$ 430 m Perimeter of rectangular field is 430 m in which fencing has to be done. ∴ Cost of fencing = Rs (430 $\times$ 2.50) ➽ Rs 1075 Hence, the cost of fencing the rectangular field is Rs 1075.

ESSAY TYPE QU12. The ratio of the length and breadth of a 16rectangular field is 3:2 and its area is 11094sq m. What will be the cost of fencing thefield at the rate of 2.50 per metre?

Answer»

✬ Cost = Rs 1075 ✬

Step-by-step explanation:

Given:

To FIND:

Solution: Let x be the common in given ratio. Therefore,

We know that the

★ Area of Rectangle = ( Length $\times$ Breadth ) sq units ★

But A/q

$\implies{\rm }$ 11094 = ( Length $\times$ Breadth )

$\implies{\rm }$ 11094 = ( 3x $\times$ 2x )

$\implies{\rm }$ 11094 = 6x²

$\implies{\rm }$ 11094/6 = x²

$\implies{\rm }$ 1849 = x²

$\implies{\rm }$ √1849 = x

$\implies{\rm }$ √43 $\times$ 43 = x

$\implies{\rm }$ 43 m = x

So,

➟ Length = 3x = 3 $\times$ 43 = 129 m

➟ Breadth = 2x = 2 $\times$ 43 = 86 m

Since, fencing will be done in perimeter of rectangular field.

★ Perimeter = 2 ( Length + Breadth ) ★

$\implies{\rm }$ 2 ( 129 + 86 )

$\implies{\rm }$ 2 $\times$ 215

$\implies{\rm }$ 430 m

Perimeter of rectangular field is 430 m in which fencing has to be done.

∴ Cost of fencing = Rs (430 $\times$ 2.50)

➽ Rs 1075

Hence, the cost of fencing the rectangular field is Rs 1075.