ShmoopTube

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Here’s your shmoop du jour, brought to you by parallelograms.

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The Leaning Tower of Pisa of rectangles.

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Given that ABCD is a parallelogram, find the value of y.

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Here are the potential answers...

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Well, we’re really only given one piece of information, other than in the diagram…

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…which is that we’re looking at a parallelogram.

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We know a few things about parallelograms…and one of those things is going to help us a ton here.

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Opposite sides of a parallelogram are always equal in length.

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That tells us that 6x – 6 = 4x + 5…

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…and 8y + 3 = x – 5.

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We’ll start with the first one so we can nail down the value of x.

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Watch your fingers.

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If we subtract 4x from both sides…

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…and add 6 to both sides…

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…we get 2x = 11.

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Dividing both sides now by 2, we see that x = 11/2.

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Now we can take that value and throw it into our other equation…

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…which becomes 8y + 3 = 11/2 – 5.

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5 can be rewritten as 10/2…and 11/2 minus 10/2 is just… 1/2.

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We can subtract 3 from both sides to get 8y = -2 1/2.

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When dividing both sides by 8, we may want to rewrite that part on the right as -5/2,

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to make things easier.

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-5/2 divided by 8 is the same as multiplying it by 1/8…

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…which comes out to -5/16.

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Answer C.

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