Answer:
21 cm wide by 5 cm long
Explanation:
The given relation and the formula for the perimeter of a rectangle can be used to find the dimensions.
Setup
Let x represent the length of the rectangle. Then the width is 3(x+2). The perimeter is given by the formula ...
P = 2(L +W)
Using the given value of perimeter and the dimensions we have defined, we get ...
52 = 2(x +(3(x +2)))
Solution
Simplifying the equation gives ...
52 = 8x +12
40 = 8x . . . . . . subtract 12
5 = x . . . . . . . . divide by 8; the rectangle's length
3(x+2) = 3(7) = 21 . . . . the rectangle's width
The rectangle is 5 cm long and 21 cm wide.
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Additional comment
The only thing the reference to odd integers contributes is the fact that consecutive odd integers differ by 2. That is why we use 3(x+2) for "3 times the next consecutive odd integer."