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The algebraic expression that will represent the perimeter in centimeters of the given rectangle is:  [tex](25.8x +11.2) $ cm[/tex]

Recall:

Perimeter of a rectangle = 2(L + W)

Given the following dimension of a rectangle:

  • width (W) = (8.4x + 2.2) cm
  • length (L) = (4.5x + 3.4) cm

To find the expression that represents the perimeter, plug in the given values into the formula for perimeter.

  • Thus:

Perimeter = [tex]2((4.5x + 3.4) + (8.4x + 2.2))[/tex]

  • Open the bracket

Perimeter = [tex]2(4.5x + 3.4 + 8.4x + 2.2)[/tex]

  • Add like terms together

Perimeter = [tex]2(12.9x + 5.6)[/tex]

  • Multiply

Perimeter = [tex]25.8x +11.2[/tex]

Therefore, the algebraic expression that will represent the perimeter in centimeters of the given rectangle is:  [tex](25.8x +11.2) $ cm[/tex]

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