# A parallelogram has sides with lengths of #14 # and #9 #. If the parallelogram's area is #56 #, what is the length of its longest diagonal?

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To find the length of the longest diagonal (d) of the parallelogram, you can use the formula for the area of a parallelogram:

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

Given that the area is 56 and the base is 14, you can find the height (h) of the parallelogram:

[ 56 = 14 \times h ] [ h = \frac{56}{14} ] [ h = 4 ]

Now, using the Pythagorean theorem, the length of the longest diagonal (d) can be found as:

[ d = \sqrt{14^2 + 4^2} ] [ d = \sqrt{196 + 16} ] [ d = \sqrt{212} ] [ d = \sqrt{4 \times 53} ] [ d = 2\sqrt{53} ]

So, the length of the longest diagonal of the parallelogram is (2\sqrt{53}).

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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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