A parallelogram has sides with lengths of #16 # and #5 #. If the parallelogram's area is #48 #, what is the length of its longest diagonal?
Length of its longest diagonal is
Then larger diagonal of parallelogram would be given by
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To find the length of the longest diagonal of a parallelogram, you can use the formula:
[ \text{Area} = \text{Base} \times \text{Height} ]
For a parallelogram, the base can be any of its sides. Let's assume the side of length 16 as the base and the side of length 5 as the height. Therefore, we have:
[ 48 = 16 \times \text{Height} ]
Solving for the height:
[ \text{Height} = \frac{48}{16} = 3 ]
Now, to find the length of the longest diagonal, you can use the Pythagorean theorem, since the diagonals of a parallelogram bisect each other:
[ \text{Longest diagonal} = \sqrt{16^2 + (2 \times \text{Height})^2} ]
Substituting the values:
[ \text{Longest diagonal} = \sqrt{16^2 + (2 \times 3)^2} = \sqrt{256 + 36} = \sqrt{292} ]
Therefore, the length of the longest diagonal of the parallelogram is ( \sqrt{292} ).
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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.
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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