# A parallelogram has sides with lengths of #24 # and #9 #. If the parallelogram's area is #14 #, what is the length of its longest diagonal?

Since the

and (relative to side with length

By the Pythagorean Theorem

and the longest diagonal is

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

[ \text{Longest diagonal} = \sqrt{a^2 + b^2 + 2ab \cos(\theta)} ]

Where (a) and (b) are the lengths of the sides of the parallelogram, and (\theta) is the angle between the sides.

Given (a = 24) and (b = 9), we first find the angle (\theta) using the formula for the area of a parallelogram:

[ \text{Area} = ab \sin(\theta) ]

Thus, (\sin(\theta) = \frac{\text{Area}}{ab} = \frac{14}{24 \times 9}).

Now, we can find (\cos(\theta)) using the identity (\sin^2(\theta) + \cos^2(\theta) = 1).

Then, we can calculate the length of the longest diagonal using the formula above.

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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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