Answer:
- length = 13 cm
- width = 11 cm
Explanation:
You want the length and width of a rectangle with perimeter 48 cm that is 2 cm longer than wide.
Setup
Let the width be represented by w. Then the length is (w+2), and the perimeter is ...
P = 2(L+W)
48 = 2((w+2) +w) . . . . . substitute for length and width and perimeter
Solution
48 = 4w +4 . . . . . . . . simplify
44 = 4w . . . . . . . . . subtract 4
11 = w . . . . . . . . . divide by 4
w+2 = 11 +2 = 13 . . . . length
The length and width of the rectangle are 13 cm and 11 cm, respectively.
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Additional comment
The sum of length and width of a rectangle is half the perimeter, so this problem can be thought of as a "sum and difference" problem. The sum of length and width is 48/2 = 24 cm. Their difference is 2 cm.
The length and width are half the sum of these numbers, and half their difference: (24+2)/2 = 13; (24-2)/2 = 11. This is the generic solution for any sum and difference problem.