Question

doo the question in copy​

Answer 1

Given :

Given that, 576m² is area the square field that Rakhi has. Also, in Rakhi's rectangular field, the length is twice it's breadth and has the same perimeter that is equal to the perimeter of the square field.

To find :

We have to find :

• Perimeter of the rectangular field
• Length of the wire used one time around the boundary of the square field
• Length of the rectangular field
• Area of the rectangular field

Explaination :

In the question, the area of the square is 576m². The rectangular field has a length that is twice the breadth and also the rectangular field has the same perimeter that of the square field. For this, first we shall find the side of the square, then find it's perimeter. Now, we should form an equation by taking unknown variables for length and breadth for the rectangle, equate it to the square field's perimeter and then find the length, breadth of the rectangle.

Solution :

Finding the side of the square field :

• Area of the square = s² units²
• 576m² = s²
• √576m² = s
• 24m = s

Finding perimeter of the square field :

• Perimeter of the square = 4s
• Perimeter = 4(24m)
• Perimeter = 96m

Length of the wire used one time around the boundary of the square field :

• Length used one time = Perimeter
• Length of the wire = 96m

Finding the length and breadth of the rectangular field :

Let, the breadth of the rectangle be x and the length of the rectangle be 2x according to the question.

Also, the rectangle field's perimeter is equal to the square field's perimeter as mentioned in the question.

• Perimeter of rectangle = 2(l+b)
• 96m = 2(x+2x)
• 96m = 2(3x)
• 96 = 6x
• 96/6 = x
• 16 = x

Finding length and breadth by substituting :

• Breadth = 16m
• Length = 2x = 32m

Finding area of the rectangular field:

• Area of rectangle = lb
• Area = 16m(32m)
• Area = 512m²

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Therefore the answers are :

• (a) (I) 96m
• (b) (II) 96m
• (c) (I) 32m
• (d) (III) 512m²