Questions on Geometry: Parallelograms answered by real tutors!

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Question 168190: Use given information to find length of all sides. Parallelograms perimeter = 48inches. side AB is 5 inches less than side BC. The long sides are AB and CD and the short sides are DA and BC. I have no idea where to start other than BC-AB=48: Use given information to find length of all sides. Parallelograms perimeter = 48inches. side AB is 5 inches less than side BC. The long sides are AB and CD and the short sides are DA and BC. I have no idea where to start other than BC-AB=48
Answer by 303795(562) About Me  (Show Source):
You can put this solution on YOUR website!
There seems to be an error on the problem as it is written if AB is the long side and it is 5 shorter than the short side.
The general idea is to draw the parallelogram first and label all the vertices. Define the length of the short side to be x inches long so write x alongside each of the two shorter sides. The longer side is 5 inches longer than a short side so it will be x + 5 inches long. Mark in the lengths of the two long sides.
To find the perimeter of the shape add up each of the sides. This will give x + (x + 5) + x + (x + 5) which you already know must equal 48.
x + (x + 5) + x + (x + 5) = 48
x + x + 5 + x + x + 5 = 48
4x + 10 = 48
4x = 38
x = 9.5
This means that the short sides are 9.5 inches long and the longer sides are 5 inches longer ie 14.5 inches. Check to make sure that the sides give a total perimeter of 48 inches.