# A parallelogram has sides with lengths of #24 # and #9 #. If the parallelogram's area is #144 #, what is the length of its longest diagonal?

Length of its longest diagonal is

Then larger diagonal of parallelogram would be given by

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The length of the longest diagonal of the parallelogram can be found using the formula:

Diagonal^2 = Side1^2 + Side2^2 + 2 * Side1 * Side2 * cos(angle between them)

Given that the sides of the parallelogram are 24 and 9, and the area is 144, we can find the angle between them using the area formula:

Area = Side1 * Side2 * sin(angle between them)

After finding the angle, substitute it into the diagonal formula to find the length of the longest diagonal.

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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 area of the parallelogram is 144 and one of its sides (base) is 24, we can rearrange the formula to solve for the height:

[ \text{Height} = \frac{\text{Area}}{\text{Base}} ]

[ \text{Height} = \frac{144}{24} = 6 ]

Now, since the height of a parallelogram is perpendicular to its base, it forms a right triangle with the longest diagonal (the hypotenuse) and half of the other side (the base). Using the Pythagorean theorem, we can find the length of the longest diagonal:

[ \text{Longest diagonal}^2 = \text{base}^2 + \text{height}^2 ]

[ \text{Longest diagonal}^2 = 24^2 + 6^2 = 576 + 36 = 612 ]

[ \text{Longest diagonal} = \sqrt{612} \approx 24.7 ]

Therefore, the length of the longest diagonal of the parallelogram is approximately 24.7 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.

- A parallelogram has sides with lengths of #5 # and #9 #. If the parallelogram's area is #27 #, what is the length of its longest diagonal?
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- What is the area of a parallelogram with corners at these coordinates on a plane: (-2,-1), (-12,-4), (9,-4), (-1,-7)?
- Two rhombuses have sides with lengths of #12 #. If one rhombus has a corner with an angle of #pi/12 # and the other has a corner with an angle of #pi/2 #, what is the difference between the areas of the rhombuses?
- A parallelogram has sides with lengths of #9 # and #8 #. If the parallelogram's area is #36 #, what is the length of its longest diagonal?

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