# Two opposite sides of a parallelogram each have a length of #6 #. If one corner of the parallelogram has an angle of #(3 pi)/4 # and the parallelogram's area is #27 #, how long are the other two sides?

The other two sides are 6.3649 long each

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To find the lengths of the other two sides of the parallelogram, we can use the formula for the area of a parallelogram, which is given by the product of the base and the height.

Given that the area of the parallelogram is 27, and one side has a length of 6, we can find the height of the parallelogram by dividing the area by the length of the given side:

Height = Area / Length of given side = 27 / 6 = 4.5

Now, we have the height of the parallelogram. To find the lengths of the other two sides, we can use trigonometric functions. Since one corner of the parallelogram has an angle of (3π)/4, and the opposite side has a length of 6, we can use the sine and cosine functions.

The length of one of the other sides can be found using the sine function:

Length of other side = Length of given side * sin(angle) = 6 * sin((3π)/4) = 6 * (-√2/2) = -3√2

The length of the other side will also be -3√2 due to the properties of a parallelogram.

Therefore, the lengths of the other two sides of the parallelogram are both -3√2.

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