Answer:
Explanation:
The given relation between length and width can be written as an equation. Let w represent the width. Then the length is 2w+2 and the area is ...
A = LW
A = (2w+2)(w) = 24
w(w+1) = 12 . . . . . . divide by 2
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We know factors of 12 are ...
12 = 1(12) = 2(6) = 3(4)
We see that 4 = 3+1, so ...
w = 3
2w+2 = 8
The dimensions of the rectangle are 3 cm wide by 8 cm long.
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Additional comment
The given quadratic also has negative solution w=-4. Negative values for geometric lengths are extraneous solutions.