Question

in parallelogram abcd, \\(\overline{bc}\\) is twice as long as \\(\overline{dc}\\). what is the perimeter of the parallelogram? (not drawn to scale) a 162 b 1164 c 324 d 5832

Explanation:

Step1: Use the property of parallelogram

In a parallelogram \(ABCD\), \(AB = DC\) and \(BC = AD\). Given \(BC = 2DC\), \(AB=8m + 60\), \(DC = 9m\). So \(8m+60=9m\).

Step2: Solve for \(m\)

Subtract \(8m\) from both sides of the equation \(8m + 60=9m\). We get \(m=60\).

Step3: Find the lengths of the sides

\(DC=9m = 9\times60=54\), \(BC = 2DC=2\times54 = 108\).

Step4: Calculate the perimeter

The perimeter \(P\) of a parallelogram is \(P = 2(DC + BC)\). Substitute \(DC = 54\) and \(BC=108\) into the formula. \(P=2(54 + 108)=2\times162 = 324\).

Answer:

C. 324