Question

The Side of rectangular park are in the ratio 4:3.
If its area is 1728m2,find its perimeter and the cost of fencing it at the rate of Rs. 60 per metre.​

Answer 1

Answer :

• Perimeter of rectangular park is 168m
• Rs.10080 is the cost of fencing it at the rate of Rs.60 per metre.

Given :

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

To find :

• Perimeter of rectangular park
• Cost of fencing it at the rate of Rs.60 per metre

Solution :

Given,

• The sides of rectangular park are in the ratio is 4:3 so,

• Let the length be 4x
• Let the breadth be 3x

Given , Area of rectangular park is 1728m².

We know that

• Area of rectangular park = l × b

Where,

• l is length of rectangular park
• b is breadth of rectangular park

↝ Area of rectangular park = length × breadth

↝ 1728 = 4x × 3x

↝1728 = 12x²

↝ 12x² = 1728

↝ x² = 1728/12

↝ x² = 144

↝ x = √144

↝ x = 12

Finding the length and breadth of rectangular park :

↝ Length = 4x

↝ Length = 4(12)

↝ Length = 48m

Length of rectangular park is 48m.

↝ Breadth = 3x

↝ Breadth = 3(12)

↝ Breadth = 36m

Breadth of rectangular park is 36m.

Finding the perimeter of rectangular park :

• Length of rectangular park is 48m
• Breadth of rectangular park is 36m

We know that

• Perimeter of rectangular park = 2(l + b)

Where,

• l is length of rectangular park
• b is breadth of rectangular park

↝ Perimeter of rectangular park = 2(l + b)

↝ Perimeter of rectangular park = 2(48 + 36)m

↝ Perimeter of rectangular park = 2(84)m

↝ Perimeter of rectangular park = 168m

Perimeter of rectangular park is 168m.

Finding the cost of fencing :

Given,

• Cost of fencing it at the rate of Rs.60 per metre so,

• Rate of fencing is Rs.60

↝ Total Cost = Perimeter of rectangular park × rate of fencing

↝ 168 × 60

↝ 10080 Rs.

Rs.10080 is the cost of fencing it at the rate of Rs.60 per metre.

Hence,

• Perimeter of rectangular park is 168m
• Rs.10080 is the cost of fencing it at the rate of Rs.60 per metre.

Answer 2

To find : Perimeter of rectangular park  and its cost of fencing at the rate of Rs.$60$ per meter .​

Given : Side of rectangular park are in the ratio $4:3$ . Its area is $1728 \ m^{2}$ .

Solution :

• As per given data we know that sides of rectangular park are in the ratio $4:3$ . Its area is $1728 \ m^{2}$ .
• Let , $4x$ and $3x$ be sides of rectangle .
• To find perimeter we use following formula :
• Area of rectangle = $l\times b$

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

• Now , sides of rectangle are :

       $4x = 4\times 12 = 48\ m \\3x = 3\times 12 =36\ m$  

• Hence , length is $48\ m$ and breadth is $36\ m$ .

• Now , Perimeter of rectangle = $2 (l +b )$

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

• Cost of fencing rectangular park = $(168 \times 60 )\ Rs$

                                                               $= 10080 \ Rs$

Hence , perimeter of  rectangular park is $168\ m$ and cost of fencing rectangular park is $10080\ Rs$ .