Question

The perimeter of a rectangle is 52 centimeters. Find the length and width if the length

is an odd integer and the width is 3 times the next consecutive odd integer
Length=_centimeters
Width=_centimeters

Answer 1

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."