# A parallelogram has sides with lengths of #16 # and #9 #. If the parallelogram's area is #81 #, what is the length of its longest diagonal?

Approximately

Referring to the diagram, this solution boils down to three elemental steps:

1. Find length of

2. Find the length of

3. Apply the Pythagoras theorem for one more time to find the length of

Step One: Find

Step Two: Find

Apply the Pythagoras theorem in

Step Three: Find

Apply the Pythagoras theorem one more time in

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Length of longer diagonal is

We know the area of the parallelogram as

Longer diagonal can be found by applying cosine law:

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To find the length of the longest diagonal of a parallelogram, you can use the formula:

Longest diagonal = √(a^2 + b^2 + 2ab)

Where 'a' and 'b' are the lengths of the sides of the parallelogram.

Given: a = 16 b = 9

Plugging in the values: Longest diagonal = √(16^2 + 9^2 + 2 * 16 * 9)

Longest diagonal = √(256 + 81 + 288)

Longest diagonal = √(625)

Longest diagonal = 25

Therefore, the length of the longest diagonal of the parallelogram is 25 units.

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To find the length of the longest diagonal of a parallelogram, you can use the formula:

[ \text{Diagonal} = \sqrt{(side1)^2 + (side2)^2 + 2 \times side1 \times side2} ]

Given the sides of the parallelogram as 16 and 9, and the area as 81, we can use the formula for area of a parallelogram:

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

[ 81 = 16 \times \text{height} ]

[ \text{height} = \frac{81}{16} ]

Now, substituting these values into the formula for the diagonal:

[ \text{Diagonal} = \sqrt{16^2 + 9^2 + 2 \times 16 \times 9} ]

[ \text{Diagonal} = \sqrt{256 + 81 + 288} ]

[ \text{Diagonal} = \sqrt{625} ]

[ \text{Diagonal} = 25 ]

So, the length of the longest diagonal of the parallelogram is 25.

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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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