# A parallelogram has sides with lengths of #15 # and #8 #. If the parallelogram's area is #12 #, what is the length of its longest diagonal?

Length of longest diagonal

Using a side of length

since the area is

the height relative to a side of length

The required diagonal (

the hypotenuse of a right triangle formed by extending the base by an amount

The length of this extension (

The requested diagonal now can also be calculated using the Pythagorean Theorem as:

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

( \text{Longest diagonal} = \sqrt{(a^2 + b^2 + 2ab \cdot \cos(\theta))} )

Where:

- ( a ) and ( b ) are the lengths of the sides of the parallelogram,
- ( \theta ) is the angle between the sides.

Given that the sides of the parallelogram have lengths of 15 and 8, and the area is 12, you can calculate the angle between the sides using the formula:

( \text{Area} = ab \cdot \sin(\theta) )

By substituting the given values, you can solve for ( \theta ). Once you have ( \theta ), you can find the length of the longest diagonal using the formula for the longest diagonal.

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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.

- Two rhombuses have sides with lengths of #15 #. If one rhombus has a corner with an angle of #(3pi)/8 # and the other has a corner with an angle of #(5pi)/6 #, what is the difference between the areas of the rhombuses?
- A parallelogram has sides A, B, C, and D. Sides A and B have a length of #2 # and sides C and D have a length of # 9 #. If the angle between sides A and C is #(3 pi)/8 #, what is the area of the parallelogram?
- How do you tessellate a quadrilateral?
- A parallelogram has sides with lengths of #15 # and #12 #. If the parallelogram's area is #42 #, what is the length of its longest diagonal?
- Two opposite sides of a parallelogram each have a length of #1 #. If one corner of the parallelogram has an angle of #(3 pi)/4 # and the parallelogram's area is #24 #, how long are the other two sides?

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