SOLUTION: The perimeter of parallelogram ABCD is 96 cm. AD is 6 cm more than twice AB. Find the lengths of all four sides of ABCD.

Algebra ->  Pythagorean-theorem -> SOLUTION: The perimeter of parallelogram ABCD is 96 cm. AD is 6 cm more than twice AB. Find the lengths of all four sides of ABCD.      Log On


   

Question 1154093: The perimeter of parallelogram ABCD is 96 cm. AD is 6 cm more than twice AB. Find the lengths of all four sides of ABCD.
Found 2 solutions by josgarithmetic, MathLover1:
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
2x+6 and x, two on the non opposite sides

2%282x%2B6%29%2B2x=96
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Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

The perimeter of parallelogram ABCD+is 96cm.
AD is 6cm more than twice AB.
so, AD=2AB%2B6.....eq.1
in parallelogram opposite sides are equal in length:
AB=CD
AD=BC=>BC=2AB%2B6
P=96cm
AB%2BCD%2BAD%2BBC=96.....substitute AB=CD,AD and BC from eq.1
AB%2BAB%2B2AB%2B6%2B2AB%2B6=96
6AB%2B12=96
6AB=96-12
6AB=84
AB=84%2F6
highlight%28AB=14%29 => also highlight%28CD=14%29

go to eq.1
AD=2AB%2B6.....eq.1, substitute AB
AD=2%2A14%2B6
highlight%28AD=34%29=> also highlight%28BC=34%29

check the perimeter:
AB%2BCD%2BAD%2BBC=96
14%2B14%2B34%2B34=96
96=96