Question

the perimeter of parallelogram abcd is 46 inches. what is da?
3 in.
4 in.
8 in.
19 in.
not drawn to scale

Explanation:

Step1: Use the property of parallelogram

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

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Step2: Calculate \(AB\) and \(CD\)

Substitute \(x = 3\) into \(AB=(8x - 5)\), \(AB=8\times3-5=24 - 5=19\) inches. Substitute \(x = 3\) into \(CD=(3x + 10)\), \(CD=3\times3+10=9 + 10=19\) inches.

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

We know \(P = 46\) inches and \(P=2(AB + AD)\). Substitute \(AB = 19\) and \(P = 46\) into the formula \(46=2(19+AD)\).

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Answer:

\(4\) in.