# A parallelogram has sides with lengths of #9 # and #8 #. If the parallelogram's area is #32 #, what is the length of its longest diagonal?

It is

Consider the image. From the initial data we have

We know that the area is

For the longest diagonal we need to know

Finally, the diagonal is

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

Longest diagonal length = √(a^2 + b^2 + 2ab)

Where 'a' and 'b' are the lengths of the sides of the parallelogram.

Given: a = 9 b = 8

Using the formula:
Longest diagonal length = √(9^2 + 8^2 + 2*9*8)

Longest diagonal length = √(81 + 64 + 144)

Longest diagonal length = √289

Longest diagonal length ≈ 17

So, the length of the longest diagonal of the parallelogram is approximately 17 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 #16 # and #15 #. If the parallelogram's area is #64 #, what is the length of its longest diagonal?
- Two opposite sides of a parallelogram each have a length of #8 #. If one corner of the parallelogram has an angle of #(5 pi)/6 # and the parallelogram's area is #44 #, how long are the other two sides?
- Two rhombuses have sides with lengths of #7 #. If one rhombus has a corner with an angle of #pi/6 # and the other has a corner with an angle of #(pi)/4 #, what is the difference between the areas of the rhombuses?
- How can I prove that two quadrilaterals are congruent to one another?
- Which types of quadrilateral have exactly three right angles?

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