# A parallelogram has sides with lengths of #16 # and #8 #. If the parallelogram's area is #80 #, what is the length of its longest diagonal?

longest diagonal

From the given: two sides 16 and 8 and area=80, are enough to compute for the height h of the parallelogram.

Compute the larger interior angle: Let that angle be X

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To find the length of the longest diagonal of the parallelogram, we can use the formula for the area of a parallelogram:

Area = base × height

Since the sides of the parallelogram are given as 16 and 8, and the area is given as 80, we can find the height of the parallelogram using the formula:

(80 = 16 \times \text{height})

Solving for the height:

(\text{height} = \frac{80}{16} = 5)

Now, the longest diagonal of a parallelogram can be found using the Pythagorean theorem. In a parallelogram, the diagonals bisect each other and form right angles.

Let (d) be the length of the longest diagonal. Then, according to the Pythagorean theorem:

(d^2 = (\text{side})^2 + (\text{height})^2)

Substituting the values:

(d^2 = 16^2 + 5^2)

(d^2 = 256 + 25)

(d^2 = 281)

Therefore, (d = \sqrt{281}) or approximately (16.76).

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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.

- A parallelogram has sides A, B, C, and D. Sides A and B have a length of #7 # and sides C and D have a length of # 2 #. If the angle between sides A and C is #(3 pi)/4 #, what is the area of the parallelogram?
- Two rhombuses have sides with lengths of #16 #. If one rhombus has a corner with an angle of #pi/12 # 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 with lengths of #14 # and #9 #. If the parallelogram's area is #56 #, what is the length of its longest diagonal?
- Two opposite sides of a parallelogram each have a length of #14 #. If one corner of the parallelogram has an angle of #(3 pi)/4 # and the parallelogram's area is #70 #, how long are the other two sides?
- Two opposite sides of a parallelogram each have a length of #8 #. If one corner of the parallelogram has an angle of #( pi)/3 # and the parallelogram's area is #36 #, how long are the other two sides?

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