A parallelogram has sides with lengths of #15 # and #12 #. If the parallelogram's area is #120 #, what is the length of its longest diagonal?

Answer 1

There is no formula for the area of parallelogram with its diagonals.So, there are no answers for this

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Answer 2

#=25.24#

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Answer 3

To find the length of the longest diagonal of the parallelogram, you can use the formula for the area of a parallelogram:

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

Given that the area is ( 120 ) and one of the sides (the base) is ( 15 ), you can find the height of the parallelogram:

[ \text{Area} = 120 ] [ \text{Base} = 15 ]

[ \text{Height} = \frac{\text{Area}}{\text{Base}} = \frac{120}{15} = 8 ]

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 sides of the parallelogram:

[ \text{Longest diagonal}^2 = \text{Height}^2 + \text{Side}^2 ]

Since the parallelogram is symmetrical, both diagonals have the same length. Therefore:

[ \text{Longest diagonal} = \sqrt{\text{Height}^2 + \text{Side}^2} ]

[ \text{Longest diagonal} = \sqrt{8^2 + 12^2} = \sqrt{64 + 144} = \sqrt{208} ]

Therefore, the length of the longest diagonal of the parallelogram is ( \sqrt{208} ).

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Answer from HIX Tutor

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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