# A parallelogram has sides with lengths of #14 # and #15 #. If the parallelogram's area is #63 #, what is the length of its longest diagonal?

Find the height, then use Pythagoras in two different right-angled triangles to get the length of the longer diagonal

Draw a sketch of the parallelogram first, extend the base and draw in the height to meet the extended base. There are two right-angled triangles formed.

Find the height of the parallelogram. A = b x h

Working in the right-angled triangle outside the parallelogram with Hypotenuse = 14 and height = 4.2, gives the following:

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The length of the longest diagonal of the parallelogram is 19.

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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 with lengths of #15 # and #8 #. If the parallelogram's area is #12 #, what is the length of its longest diagonal?
- A parallelogram has sides A, B, C, and D. Sides A and B have a length of #6 # and sides C and D have a length of # 3 #. If the angle between sides A and C is #(3 pi)/4 #, what is the area of the parallelogram?
- Two opposite sides of a parallelogram have lengths of #8 #. If one corner of the parallelogram has an angle of #pi/8 # and the parallelogram's area is #32 #, how long are the other two sides?
- Two opposite sides of a parallelogram each have a length of #25 #. If one corner of the parallelogram has an angle of #(5 pi)/12 # and the parallelogram's area is #175 #, how long are the other two sides?
- A parallelogram has sides A, B, C, and D. Sides A and B have a length of #5 # and sides C and D have a length of # 8 #. If the angle between sides A and C is #(5 pi)/8 #, what is the area of the parallelogram?

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