Question

the perimeter of the parallelogram below is 32.2. what equation would you set up to solve for x? what is the value of x? round her answer and round to the nearest tenth if necessary. 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. 2.7

Explanation:

Step1: Recall perimeter formula for parallelogram

The perimeter \(P\) of a parallelogram is \(P = 2(a + b)\), where \(a\) and \(b\) are the lengths of adjacent - sides. Here, \(a=3x - 8\) and \(b = 16\), and \(P=32.2\). So the equation is \(2((3x - 8)+16)=32.2\), which simplifies to \((3x - 8)+16+(3x - 8)+16 = 32.2\).

Step2: Simplify the equation

First, combine like - terms: \((3x+3x)+(-8 - 8 + 16+16)=32.2\), which gives \(6x+16 = 32.2\). Then, subtract 16 from both sides: \(6x=32.2 - 16\), so \(6x = 16.2\).

Step3: Solve for \(x\)

Divide both sides of the equation \(6x = 16.2\) by 6: \(x=\frac{16.2}{6}=2.7\).

Answer:

The equation is B. \(3x - 8+16+3x - 8+16 = 32.2\) and \(x = 2.7\), so the answer is B, F.