Questions: Tennessee Geometry Sem2 Quiz 3.2.1 - Properties of Parallelograms The perimeter of the parallelogram below is 32.2. What equation would you set up to solve for x? Wh is the value of x? Select two answer and round to the nearest tenth if necessary. [mark all correct answers] a. 3x-8+16=32.2 b. 3x-8+16+3x-8+16=32.2 c. 3x-8=16+32.2 d. 8 e. 5.3 f. 27

Tennessee Geometry Sem2 Quiz 3.2.1 - Properties of Parallelograms The perimeter of the parallelogram below is 32.2. What equation would you set up to solve for x? Wh is the value of x? Select two answer and round to the nearest tenth if necessary. [mark all correct answers] a. 3x-8+16=32.2 b. 3x-8+16+3x-8+16=32.2 c. 3x-8=16+32.2 d. 8 e. 5.3 f. 27
Transcript text: Tennessee Geometry Sem2 Quiz 3.2.1 - Properties of Parallelograms The perimeter of the parallelogram below is 32.2. What equation would you set up to solve for $x$ ? Wh is the value of $x$ ? Select two answer and round to the nearest tenth if necessary. [mark all correct answers] a. $3 x-8+16=32.2$ b. $3 x-8+16+3 x-8+16=32.2$ c. $3 x-8=16+32.2$ d. 8 e. 5.3 f. 27
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Solution

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Solution Steps

Step 1: Understand the Problem

The problem involves finding the value of \( x \) in a parallelogram where the perimeter is given as 32.2. The sides of the parallelogram are labeled with expressions involving \( x \).

Step 2: Identify the Sides of the Parallelogram

In the parallelogram \( URST \):

  • \( UR \) and \( TS \) are each 16 units.
  • \( UT \) and \( RS \) are each \( 3x - 8 \) units.
Step 3: Set Up the Perimeter Equation

The perimeter of a parallelogram is the sum of all its sides. Therefore, the equation for the perimeter is: \[ 2(16) + 2(3x - 8) = 32.2 \]

Step 4: Simplify the Equation

Simplify the equation to solve for \( x \): \[ 32 + 6x - 16 = 32.2 \] \[ 6x + 16 = 32.2 \] \[ 6x = 32.2 - 16 \] \[ 6x = 16.2 \]

Step 5: Solve for \( x \)

Divide both sides by 6 to find \( x \): \[ x = \frac{16.2}{6} \] \[ x = 2.7 \]

Final Answer

The correct equation to set up is: \[ 3x - 8 + 16 + 3x - 8 + 16 = 32.2 \] The value of \( x \) is: \[ x = 2.7 \]

So, the correct answers are:

  • b. \( 3x - 8 + 16 + 3x - 8 + 16 = 32.2 \)
  • f. \( 2.7 \)
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