Question

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

Answer 1

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Answer 2

✬ 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.