# A parallelogram has sides with lengths of #14 # and #8 #. If the parallelogram's area is #49 #, what is the length of its longest diagonal?

Find the height, then use Pythagoras twice - first to find the length of the extended base, then to find the length of the longer diagonal.

Diagonal =

Draw a sketch of the parallelogram first!

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

Working in the right-angled triangle outside the parallelogram with Hypotenuse = 8 and height = 3.5 , gives the following:

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To find the length of the longest diagonal of a parallelogram with given side lengths, you can use the formula:

[ \text{Area} = \text{base} \times \text{height} ]

Given that the area of the parallelogram is 49 and one of the sides (base) is 14, you can find the height using the formula:

[ \text{Height} = \frac{\text{Area}}{\text{Base}} ]

[ \text{Height} = \frac{49}{14} = 3.5 ]

Now, using the Pythagorean theorem, you can find the length of the longest diagonal (which is the hypotenuse of a right triangle formed by the two sides and the height):

[ \text{Longest diagonal} = \sqrt{(\text{Base})^2 + (\text{Height})^2} ]

[ \text{Longest diagonal} = \sqrt{(14)^2 + (3.5)^2} ]

[ \text{Longest diagonal} = \sqrt{196 + 12.25} ]

[ \text{Longest diagonal} = \sqrt{208.25} ]

[ \text{Longest diagonal} \approx 14.43 ]

So, the length of the longest diagonal of the parallelogram is approximately 14.43 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.

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