# A parallelogram has sides with lengths of #16 # and #8 #. If the parallelogram's area is #24 #, what is the length of its longest diagonal?

Area of parallelogram

The length of the longest diagonal :

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To find the length of the longest diagonal of a parallelogram, you can use the formula:

Diagonal = √(side1^2 + side2^2 + 2 * side1 * side2 * cos(angle))

In this case, the lengths of the sides are given as 16 and 8, and the area is given as 24. Using the formula for the area of a parallelogram (Area = base * height), we can find the height of the parallelogram.

Area = base * height 24 = 16 * height height = 24/16 = 1.5

Now, using the formula for the longest diagonal:

Diagonal = √(16^2 + 8^2 + 2 * 16 * 8 * cos(180°))

= √(256 + 64 + 256 * (-1))

= √(320 - 256)

= √64

= 8

So, the length of the longest diagonal of the parallelogram is 8.

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To find the length of the longest diagonal of the parallelogram, we can use the formula for the area of a parallelogram:

[ \text{Area} = \text{base} \times \text{height} ]

Given that the parallelogram's area is 24 and one of its sides is 16 units, we can solve for the height:

[ 24 = 16 \times \text{height} ]

[ \text{height} = \frac{24}{16} ]

[ \text{height} = 1.5 ]

Since the height of the parallelogram is 1.5 units, and the other side is 8 units, we have formed a right triangle with the diagonal as the hypotenuse. Using the Pythagorean theorem, we can find the length of the longest diagonal ( d ):

[ d^2 = 8^2 + 1.5^2 ]

[ d^2 = 64 + 2.25 ]

[ d^2 = 66.25 ]

[ d = \sqrt{66.25} ]

[ d \approx 8.13 ]

Therefore, the length of the longest diagonal of the parallelogram is approximately 8.13 units.

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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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- 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 #36 #, how long are the other two sides?

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