Question

the perimeter of parallelogram abcd is 46 inches. what is da? 3 in. 4 in. 8 in. 19 in.

Explanation:

Step1: Use the property of parallelogram

In a parallelogram, \(AB = CD\) and \(AD = BC\). The perimeter formula for a parallelogram is \(P=2(AB + AD)\). Given \(AB=(8x - 5)\) and \(CD=(3x + 10)\), since \(AB = CD\), we have \(8x-5=3x + 10\).

$$\begin{align*} 8x-3x&=10 + 5\\ 5x&=15\\ x&=3 \end{align*}$$

Step2: Find the length of \(AB\) and \(CD\)

Substitute \(x = 3\) into \(AB=(8x - 5)\), \(AB=8\times3-5=19\) inches.

Step3: Use the perimeter formula to find \(AD\)

We know \(P = 46\) inches, and \(P=2(AB + AD)\). Substitute \(AB = 19\) into \(P=2(AB + AD)\), we get \(46=2(19+AD)\).

$$\begin{align*} \frac{46}{2}&=19 + AD\\ 23&=19+AD\\ AD&=23 - 19\\ AD&=4 \end{align*}$$

Answer:

\(4\) in.