# A parallelogram has sides with lengths of #16 # and #15 #. If the parallelogram's area is #60 #, what is the length of its longest diagonal?

Length of the longer 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 the product of the base and the height. Let's denote the lengths of the sides of the parallelogram as ( a ) and ( b ), and the length of the longest diagonal as ( d ).

Given that the sides of the parallelogram have lengths of 16 and 15, and the area is 60, we can set up the following equation:

[ 16 \cdot h = 60 ]

Solving for the height ( h ), we get:

[ h = \frac{60}{16} = \frac{15}{4} ]

Now, using the formula for the area of a parallelogram, we have:

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

[ 60 = 15 \times \frac{15}{4} ]

[ 60 = \frac{225}{4} ]

Now, we can find the length of the other diagonal using the formula for the area of a parallelogram:

[ 60 = 16 \times d ]

[ d = \frac{60}{16} = \frac{15}{4} ]

Therefore, the length of the longest diagonal of the parallelogram is also ( \frac{15}{4} ) 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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