# A parallelogram has sides with lengths of #15 # and #12 #. If the parallelogram's area is #81 #, what is the length of its longest diagonal?

The length of the longest diagonal is

The dimensions of the parrallelogram are

The

But the area of a parallelogram is

The longest diagonal is

We apply the cosine rule to the triangle

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

( \text{Area} = \text{Base} \times \text{Height} )

Given that the area of the parallelogram is 81 and the base is 12, you can rearrange the formula to solve for the height:

( 81 = 12 \times \text{Height} )

( \text{Height} = \frac{81}{12} = 6.75 )

Now, to find the length of the longest diagonal (denoted by ( d )), you can use the Pythagorean theorem, since the diagonals of a parallelogram bisect each other:

( d^2 = 15^2 + 6.75^2 )

( d^2 = 225 + 45.5625 )

( d^2 = 270.5625 )

( d = \sqrt{270.5625} )

( d \approx 16.45 )

Therefore, the length of the longest diagonal of the parallelogram is approximately 16.45.

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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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- What type of quadrilateral has four congruent sides and two obtuse angles?
- A parallelogram has sides with lengths of #16 # and #15 #. If the parallelogram's area is #144 #, what is the length of its longest diagonal?
- What is the name of a polygon that has twice as many sides as a quadrilateral?

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