# A parallelogram has sides with lengths of #12 # and #8 #. If the parallelogram's area is #64 #, what is the length of its longest diagonal?

longest diagonal =12.00053677

Using the cosine rule to find the longest diagonal

a=12.00053677

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To find the length of the longest diagonal of a parallelogram with sides of 12 and 8 and an area of 64, we can use the formula for the area of a parallelogram, which is given as base multiplied by height.

Let's denote the base of the parallelogram as 12 and the height as h. We can set up the equation:

Area = base × height 64 = 12 × h

Now, solve for h:

h = 64 / 12 h = 5.33 (rounded to two decimal places)

Now that we have the height, we can use the Pythagorean theorem to find the length of the longest diagonal. The diagonal, in a parallelogram, forms a right triangle with the base and height.

Using the Pythagorean theorem (a^2 + b^2 = c^2), where a and b are the base and height of the parallelogram respectively, and c is the length of the diagonal, we have:

a = 12 (base) b = 5.33 (height) c = diagonal (which we want to find)

Substitute the values into the Pythagorean theorem:

12^2 + 5.33^2 = c^2 144 + 28.39 = c^2 172.39 = c^2

Now, solve for c:

c = √172.39 c ≈ 13.13

Therefore, the length of the longest diagonal of the parallelogram is approximately 13.13 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.

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