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? 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

The perimeter $P$ of a parallelogram is the sum of all its side - lengths. In parallelogram $TURS$, the side - lengths are $16$, $3x - 8$, $16$, and $3x - 8$. So $P=(3x - 8)+16+(3x - 8)+16$.

Step2: Set up the equation

Since $P = 32.2$, the equation is $(3x - 8)+16+(3x - 8)+16=32.2$.

Step3: Simplify the left - hand side of the equation

Combine like terms: $(3x+3x)+(-8 - 8+16 + 16)=6x + 16$. So the equation becomes $6x+16 = 32.2$.

Step4: Solve for $x$

Subtract 16 from both sides: $6x=32.2−16=16.2$. Then divide both sides by 6: $x=\frac{16.2}{6}=2.7$.

Answer:

b. $3x - 8+16 + 3x - 8+16 = 32.2$
f. $2.7$