Chapter 5.6, Problem 8PSA

To determine

To calculate:Theside AB of parallelogram ABCD.

Answer to Problem 8PSA

The side ABis$10$ .

Explanation of Solution

Given information:

In a parallelogram ABCD,

  $\frac{AB}{BC}=\frac{5}{3}$

Perimeter of ABCD= 32.

Calculation:

  

In parallelogram opposite sides are congruent.

  $\begin{array}{l}\overline{AB}\cong \overline{CD}\\ \overline{BC}\cong \overline{AD}\end{array}$

Perimeter is sum of all sides.

Perimeter of ABCD= 32

  $\frac{AB}{BC}=\frac{5}{3}$

  $\begin{array}{l}P(▱ABCD)=AB+BC+CD+DA\\ AB+BC+CD+DA=32\\ 5x+3x+5x+3x=32\\ 16x=32\\ x=\frac{32}{16}=2\\ AB=5x\\ AB=5\times 2=10\end{array}$