# A parallelogram has sides with lengths of #7 # and #16 #. If the parallelogram's area is #32 #, what is the length of its longest diagonal?

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Using the formula for the area of a parallelogram, A = base × height, we can find the height of the parallelogram. Since the base is 16 and the area is 32, the height is 2.

The longest diagonal of a parallelogram can be found using the Pythagorean theorem. Let's denote the longest diagonal as d, and the sides of the parallelogram as a = 7 and b = 16. The diagonal d, the height h, and one side of the parallelogram form a right-angled triangle.

Using the Pythagorean theorem, (d^2 = a^2 + h^2), where h = 2 (the height we found earlier).

Substituting the values, (d^2 = 7^2 + 2^2 = 49 + 4 = 53).

Therefore, the length of the longest diagonal of the parallelogram is √53 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.

- 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 # 6 #. If the angle between sides A and C is #(7 pi)/12 #, what is the area of the parallelogram?
- Two opposite sides of a parallelogram have lengths of #15 #. If one corner of the parallelogram has an angle of #pi/4 # and the parallelogram's area is #45 #, how long are the other two sides?
- Two opposite sides of a parallelogram each have a length of #18 #. If one corner of the parallelogram has an angle of #( pi)/3 # and the parallelogram's area is #54 #, how long are the other two sides?
- In an isosceles trapezoid ABCD, AB=CD=5. The top base = 8 and the bottom base = 14. What is the area of this trapezoid?
- A parallelogram has sides with lengths of #12 # and #6 #. If the parallelogram's area is #42 #, what is the length of its longest diagonal?

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