A parallelogram has sides with lengths of #15 # and #12 #. If the parallelogram's area is #90 #, 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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The length of the longest diagonal of the parallelogram can be found using the formula:
[ \text{Longest diagonal} = \sqrt{a^2 + b^2 + 2ab \cos(\theta)} ]
where (a) and (b) are the lengths of the sides of the parallelogram and (\theta) is the angle between them.
Given (a = 15) and (b = 12), and knowing that the area of the parallelogram is given by (90), we can find the value of (\theta) using the formula for the area of a parallelogram:
[ \text{Area} = ab \sin(\theta) ]
Substituting the given values:
[ 90 = 15 \times 12 \times \sin(\theta) ]
[ \sin(\theta) = \frac{90}{180} = \frac{1}{2} ]
Thus, ( \theta = \frac{\pi}{6} ) radians.
Now, plug the values of (a), (b), and ( \theta ) into the formula for the longest diagonal:
[ \text{Longest diagonal} = \sqrt{15^2 + 12^2 + 2 \times 15 \times 12 \times \cos\left(\frac{\pi}{6}\right)} ]
[ \text{Longest diagonal} = \sqrt{225 + 144 + 360} ]
[ \text{Longest diagonal} = \sqrt{729} ]
[ \text{Longest diagonal} = 27 ]
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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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