# A parallelogram has sides with lengths of #14 # and #15 #. If the parallelogram's area is #42 #, what is the length of its longest diagonal?

Length of the longest diagonal AC = 28.8533

Given

Area of the parallelogram = l * h = 42

AE = DF = a = sqrt(w^2-h^2) = sqrt(14^2 - 2.8^2) = 13.7171#

AF = l + a = 15 + 13.7171 = 28.7171#

Longest diagonal AC

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

Longest diagonal = √(a^2 + b^2 + 2ab)

Where 'a' and 'b' are the lengths of the sides of the parallelogram. Given that the sides have lengths of 14 and 15, respectively, we can substitute these values into the formula:

Longest diagonal = √(14^2 + 15^2 + 2 * 14 * 15)

Longest diagonal ≈ √(196 + 225 + 420)

Longest diagonal ≈ √841

Longest diagonal ≈ 29

So, the length of the longest diagonal of the parallelogram is approximately 29 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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