Given that the perimeter of a rectangle is 30 cm.

We will assume that the length = L and the width = W

==> 2w + 2L = 30

==> L + w = 15 ...............(1)

Now, given that the length if twice the width.

==> L = 2w

Now we will substitute onto (2).

==> 2w + w = 15

==> 3w = 15

We will divide by 3.

==> w = 5

==> L = 2*5 = 10

Now we will calculate the area.

==> A = L*w = 10*5 = 50

**Then, the area of the rectangle is 50 cm^2**

The rectangle has a perimeter of 30 cm. Its length is twice its width. Let us denote length by L and width by W.

So we have L = 2W

Perimeter = 2L + 2W = 30

=> 2* 2W + 2W = 30

=> 4W + 2W = 30

=> 6W = 30

=> W = 5

L = 10

The area = L*W = 5* 10 = 50

**Therefore the area of the rectangle is 50 cm^2.**

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