# A parallelogram has sides with lengths of #14 # and #11 #. If the parallelogram's area is #84 #, what is the length of its longest diagonal?

Length of the longest diagonal AC = 24.6576

Given

Area of the parallelogram = l * h = 84

AE = DF = a = sqrt(w^2-h^2) = sqrt(11^2 - 6^2) = 9.2195#

AF = l + a = 14 + 9.2195 = 23.9125#

Longest diagonal AC

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You can find the length of the longest diagonal of the parallelogram using the formula:

[ \text{Area} = \frac{1}{2} \times d_1 \times d_2 ]

Given that the area is 84 and the sides are 14 and 11, you can solve for the longest diagonal (d_1):

[ 84 = \frac{1}{2} \times 14 \times d_1 ] [ 168 = 14 \times d_1 ] [ d_1 = \frac{168}{14} ] [ d_1 = 12 ]

So, the length of the longest diagonal (d_1) is 12 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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