481,487 views
21 votes
21 votes
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.

User Rudrik
by
2.5k points

1 Answer

21 votes
21 votes

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) \\ (106)/(2)=2+3AB \\ 53-2=3AB \\ (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

User Ddolce
by
2.9k points