Two opposite sides of a parallelogram each have a length of #6 #. If one corner of the parallelogram has an angle of #( pi)/3 # and the parallelogram's area is #24 #, how long are the other two sides?

Answer 1

The lengths of the other two sides are both #8/sqrt3#.

Call the parallelogram #ABCD# and let #AB=CD=6# and #m/_A=m/_C=pi/3#. We know the area of the parallelogram can be calculated by the following formula using vectors: #A=|vec (AB) xx vec (AD)|=|vec (AB)||vec (AD)|sintheta#. We are given that the area is 24, so #24=|vec (AB)||vec (AD)|sintheta# #24=6|vec (AD)|sin(pi/3)# #|vec (AD)|=4/(sqrt3/2)# #:.|vec (AD)|=8/sqrt3# Since the lengths of opposite sides in a parallelogram are equal, we know that the lengths of the other two sides are #8/sqrt3#.
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Answer 2

To find the lengths of the other two sides of the parallelogram, we can use the formula for the area of a parallelogram: Area = base * height. Since the parallelogram's area is given as 24, we can set up the equation:

24 = 6 * height

Solving for height:

height = 24 / 6 = 4

Now, to find the lengths of the other two sides, we can use the formula for the area of a parallelogram: Area = base * height. Since one side of the parallelogram is 6 and the opposite side is also 6, we have:

24 = 6 * 4

Now, let's find the length of the other two sides of the parallelogram. We know that the opposite sides of a parallelogram are equal in length, so the length of the other two sides is also 6. Therefore, the lengths of the other two sides of the parallelogram are both 6.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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