Questions: Write the polynomial that represents the perimeter of the figure pictured below. Perimeter =

Write the polynomial that represents the perimeter of the figure pictured below. Perimeter =
Transcript text: Write the polynomial that represents the perimeter of the figure pictured below. Perimeter $=$ $\square$
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Solution

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Solution Steps

Step 1: Identify the sides of the figure

The figure has six sides with the following lengths:

  • \( 8x^2 \)
  • \( 19x \)
  • \( 16x^2 \)
  • \( 9x \)
  • \( 8x^2 \)
  • \( 9x \)
Step 2: Write the expression for the perimeter

The perimeter of the figure is the sum of all its sides. Therefore, the expression for the perimeter is: \[ 8x^2 + 19x + 16x^2 + 9x + 8x^2 + 9x \]

Step 3: Combine like terms

Combine the \( x^2 \) terms and the \( x \) terms: \[ (8x^2 + 16x^2 + 8x^2) + (19x + 9x + 9x) \] \[ 32x^2 + 37x \]

Final Answer

The polynomial that represents the perimeter of the figure is: \[ 32x^2 + 37x \]

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