Question

in quadrilateral abcd, ad || bc. what must the length of segment ad be for the quadrilateral to be a parallelogram? 8 units 16 units 31 units 62 units

Explanation:

Step1: Recall parallelogram property

In a parallelogram, opposite - sides are equal. Since \(AD\parallel BC\) and for \(ABCD\) to be a parallelogram, \(AD = BC\). Let \(AD = 3x + 7\) and \(BC=5x - 9\). Then \(3x + 7=5x - 9\).

Step2: Solve for \(x\)

First, move the \(x\) - terms to one side: \(5x-3x=7 + 9\). Simplify the left - hand side to get \(2x\) and the right - hand side to get \(16\). So, \(2x=16\), and then \(x = 8\).

Step3: Find the length of \(AD\)

Substitute \(x = 8\) into the expression for \(AD\): \(AD=3x + 7\). Replace \(x\) with \(8\), then \(AD=3\times8+7=24 + 7=31\).

Answer:

31 units