A parallelogram has sides with lengths of #16 # and #9 #. If the parallelogram's area is #24 #, what is the length of its longest diagonal?

Answer 1

Length of the longest diagonal AC = 24.9193

Given #l = 16, w = 9, Area = 24#

Area of the parallelogram = l * h = 24
#:. BE = CF = h = (Area)/l = 24 / 16 = 1.5#

AE = DF = a = sqrt(w^2-h^2) = sqrt(9^2 - 1.5^2) = 8.8741#

AF = l + a = 16 + 8.8741 = 24.8741#

Longest diagonal AC #= sqrt(AF^2 + CF^2) = sqrt(24.8741^2 + 1.^2) = 24.9193#

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Answer 2

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

Area = base × height

Given that the area is 24 and the base is 16, we can rearrange the formula to solve for the height:

Height = Area / Base Height = 24 / 16 Height = 1.5

Now, using the Pythagorean theorem, we can find the length of the longest diagonal:

Diagonal = √(Base² + Height²) Diagonal = √(16² + 1.5²) Diagonal ≈ √(256 + 2.25) Diagonal ≈ √258.25 Diagonal ≈ 16.07

So, the length of the longest diagonal of the parallelogram is approximately 16.07.

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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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