Question

in quadrilateral abcd, $overline{ad}paralleloverline{bc}$. 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, \(AB = DC\). So, \(3x + 7=5x - 9\).

Step2: Solve the equation for \(x\)

Subtract \(3x\) from both sides: \(3x+7 - 3x=5x - 9-3x\), which gives \(7 = 2x-9\). Then add 9 to both sides: \(7 + 9=2x-9 + 9\), so \(16 = 2x\). Divide both sides by 2: \(x=\frac{16}{2}=8\).

Step3: Find the length of \(AD\)

We can use either the expression for \(AB\) or \(DC\). Using \(AB = 3x + 7\), substitute \(x = 8\) into it. \(AD=3\times8 + 7=24 + 7=31\).

Answer:

31 units