Question

in parallelogram abcd, what is dc? 3 in. 9 in. 13 in. 19 in.

Explanation:

Step1: Recall parallelogram property

In a parallelogram, opposite - sides are equal. So, \(AB = DC\). Given \(AB=(9x - 14)\) inches and \(DC=(3x + 4)\) inches, we set up the equation \(9x-14 = 3x + 4\).

Step2: Solve for \(x\)

Subtract \(3x\) from both sides: \(9x-3x-14=3x - 3x+4\), which simplifies to \(6x-14 = 4\). Then add 14 to both sides: \(6x-14 + 14=4 + 14\), giving \(6x=18\). Divide both sides by 6: \(x=\frac{18}{6}=3\).

Step3: Find the length of \(DC\)

Substitute \(x = 3\) into the expression for \(DC\). \(DC=3x + 4\), so \(DC=3\times3 + 4=9 + 4=13\) inches.

Answer:

13 in.