Question

6. the perimeter of parallelogram ABCD is 30 cm. AD 3 cm more then twice AB. find the length of AB.
a) 3 cm
b) 4 cm
c) 9 cm
d) 11 cm

Answer 1

Remember that a parallelogram has a pair of opposite and congruent sides, this means that the parallelogram will have two and only two determining sides for it's perimeter, and the double sum of these sides will give us the perimeter P:
\[P=2(AB +AD)\]
But now, the text says that "AD is three centimeters more than twice AC", which means:
\[AD=2AB +3\]
This relationship can be directly replaced in the formula for the perimeter, and since the given perimeter is "30", then:
\[2(AB+(2AB+3))=30\]
\[2(3AB+3)=30\]
And from there, you'll be able to find the length of the segment AB, which allows you to find the last side AD with the given relationship.

Answer 2

AB= 4cm