A parallelogram has sides with lengths of #15 # and #8 #. If the parallelogram's area is #27 #, what is the length of its longest diagonal?
The area is the cross-product of the sides:
Substitute the values for the area, A, and B:
We can use the Law of Cosines to compute the length of the longest diagonal:
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To find the length of the longest diagonal of the parallelogram, we can use the formula for the area of a parallelogram, which is given by the product of its base and height. We can set up an equation using this formula, along with the given lengths of the sides:
[ 15 \times h = 27 ]
Solving for the height (( h )), we get:
[ h = \frac{27}{15} = 1.8 ]
Now, we can use the formula for the length of a diagonal in a parallelogram, which is given by:
[ \text{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 those sides. Since we're looking for the longest diagonal, ( \theta = 0 ) and ( \cos(\theta) = 1 ).
So, the length of the longest diagonal (( d )) can be calculated as:
[ d = \sqrt{15^2 + 8^2 + 2(15)(8)(1)} ] [ d = \sqrt{225 + 64 + 240} ] [ d = \sqrt{529} ] [ d = 23 ]
Therefore, the length of the longest diagonal of the parallelogram is ( 23 ) 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.
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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