# A parallelogram has sides with lengths of #14 # and #15 #. If the parallelogram's area is #70 #, what is the length of its longest diagonal?

Length of the longest diagonal AC is 27.5967

Given

Area of the parallelogram = l * h = 70

AE = DF = a = sqrt(w^2-h^2) = sqrt(14^2 - 4.6667^2) = 13.1993#

AF = l + a = 14 + 13.1993 = 27.1993#

Longest diagonal AC

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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 the sides are 14 and 15, and the area is 70, we can use the formula for the area of a parallelogram:

Area = base × height

From this, you can find the height of the parallelogram. Then, you can use the Pythagorean theorem to find the length of the longest diagonal.

First, solve for the height:

70 = 14 × height height = 5

Then, use the Pythagorean theorem:

Longest diagonal length = √(14^2 + 15^2 + 2(14)(15)) Longest diagonal length ≈ √(196 + 225 + 420) Longest diagonal length ≈ √(841) Longest diagonal length ≈ 29

Therefore, 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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