Question

The perimeter of parallelogram ABCD is 106 cm. AD is 2 cm more than twice AB. Find the lengths of all four sides of ABCD.

Answer 1

The perimeter of parallelogram ABCD is computed as follows:

$P=2(AD+AB)$

AD is 2 cm more than twice AB, that is,

AD = 2 + 2AB

Replacing this information and P = 106 cm into the previous equation, we get:

$\begin{gathered} 106=2(2+2AB+AB) \\ 106=2(2+3AB) \\ \frac{106}{2}=2+3AB \\ 53-2=3AB \\ \frac{51}{3}=AB \\ 17cm=AB \end{gathered}$

Then, the measure of segment AD is:

AD = 2 + 2x17

AD = 2 + 34

AD = 36 cm

Side AB is opposite to side CD, then

CD = 17 cm

Side BC is opposite to side AD, then

BC = 36 cm