Data Sufficiency (DS) | Re: If parallelogram ABCD has a perimeter of 12 units and ∠ADC = 120

OFFICIAL EXPLANATION

\(ABCD\) is a parallelogram.

Let\(AB\) and\(CD\) measure\(p\) units and\(AD\) and\(BC\) measure\(q\) units and height of the parallelogram be\(h\) units

Therefore, Area of the parallelogram =\(ph\)


\(2(p + q) = 12\)
\(p + q = 6\) ------------(I)

\(∠ADC = 120^{\circ}\)
This implies\(∠BAC = ∠BCD = 60^{\circ}\)

Since ΔAED is a 30-60-90 triangle, applying the angle-side property (1:√3:2)

\(h=\frac{q√3}{2}\) and\( AE=\frac{q}{2} \)
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