Question

value: 4
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? 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. 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. In the given parallelogram, the side - lengths are \(16\) and \(3x - 8\). So, \(P=2(16+(3x - 8))\), which simplifies to \(P=(3x - 8)+16+(3x - 8)+16\). Since \(P = 32.2\), the equation is \(3x - 8+16+3x - 8+16 = 32.2\).

Step2: Solve the equation for \(x\)

First, combine like - terms in the equation \(3x - 8+16+3x - 8+16 = 32.2\).
\((3x+3x)+(-8 + 16-8 + 16)=32.2\), which gives \(6x + 16=32.2\).
Subtract \(16\) from both sides: \(6x=32.2−16\), so \(6x = 16.2\).
Divide both sides by \(6\): \(x=\frac{16.2}{6}=2.7\).

Answer:

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