length of a rectangle is twice its breadth. if ratio of the perimeter of the rctangle and 6 times its length is 1:2. find the dimensions of the rectangle

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To find the dimensions of the rectangle, let's assume the breadth of the rectangle as 'b'.

Given that the length of the rectangle is twice its breadth, we can write the length as '2b'.

The perimeter of a rectangle is given by the formula:
Perimeter = 2 * (Length + Breadth)

Substituting the length and breadth values, we have:
Perimeter = 2 * (2b + b)
Perimeter = 2 * (3b)
Perimeter = 6b

We also know that the ratio of the perimeter of the rectangle to 6 times its length is 1:2.

Mathematically, this can be expressed as:
Perimeter : (6 * Length) = 1 : 2

Substituting the values we calculated earlier, we have:
6b : (6 * 2b) = 1 : 2

Simplifying the expression, we get:
6b : 12b = 1 : 2

Now, we can equate the ratios of two quantities:
6b/12b = 1/2

Cancelling out the common factors, we have:
1/2 = 1/2

Therefore, the ratio is valid for any value of 'b'.

So the dimensions of the rectangle can be any value where:
Length = 2b
Breadth = b

For example, if 'b' is 1 unit, then the dimensions of the rectangle would be:
Length = 2 * 1 = 2 units
Breadth = 1 unit

Similarly, for 'b' is 2 units, the dimensions would be:
Length = 2 * 2 = 4 units
Breadth = 2 units

In general, the dimensions of the rectangle can be given as:
Length = 2b
Breadth = b

where 'b' can be any real number.