# A parallelogram has sides with lengths of #21 # and #12 #. If the parallelogram's area is #24 #, what is the length of its longest diagonal?

The longest diagonal is

We have a parallelogram

Area = base x height

The distance between the base of the height and the corner

Therefore,

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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 21 and 12, and the area of the parallelogram is 24, we can use the formula for the area of a parallelogram:

Area = base * height

24 = 21 * height

height = 24 / 21 = 8/7

Now, using the Pythagorean theorem, we can find the length of the longest diagonal:

Longest diagonal = √(21^2 + (8/7)^2 + 2 * 21 * (8/7))

Longest diagonal ≈ √(441 + 64/49 + 48) ≈ √(441 + 64/49 + 48) ≈ √(441 + 128/49)

Longest diagonal ≈ √(441 + 128/49) ≈ √(8939/49) ≈ √(8939)/7

Longest diagonal ≈ √(8939)/7 ≈ 11.86 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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