Answer: 49 square cm
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For any rectangle, the opposite sides are the same length.
Set the given expressions equal to x and solve to get
2x-1 = x+3
2x-x = 3+1
x = 4
So each opposite side is:
- 2x-1 = 2*4-1 = 8-1 = 7
- x+3 = 4+3 = 7
Each side being the same length (7) confirms we have the correct x value.
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Let's say L = 7 is the length and W is the unknown width.
We'll use the perimeter of a rectangle formula given below with P = 28 as the given perimeter. Solve for W.
P = 2*(L+W)
28 = 2*(7+W)
28/2 = 7+W
14 = 7+W
7+W = 14
W = 14-7
W = 7
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The rectangle has a length of L = 7 and width of W = 7, so its area is
A = L*W
A = 7*7
A = 49 square cm
Because we have the length and width as the same value, this rectangle is also a square.