# A parallelogram has sides with lengths of #16 # and #5 #. If the parallelogram's area is #48 #, what is the length of its longest diagonal?

Length of its longest diagonal is

Then larger diagonal of parallelogram would be given by

By signing up, you agree to our Terms of Service and Privacy Policy

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

[ \text{Area} = \text{Base} \times \text{Height} ]

For a parallelogram, the base can be any of its sides. Let's assume the side of length 16 as the base and the side of length 5 as the height. Therefore, we have:

[ 48 = 16 \times \text{Height} ]

Solving for the height:

[ \text{Height} = \frac{48}{16} = 3 ]

Now, to find the length of the longest diagonal, you can use the Pythagorean theorem, since the diagonals of a parallelogram bisect each other:

[ \text{Longest diagonal} = \sqrt{16^2 + (2 \times \text{Height})^2} ]

Substituting the values:

[ \text{Longest diagonal} = \sqrt{16^2 + (2 \times 3)^2} = \sqrt{256 + 36} = \sqrt{292} ]

Therefore, the length of the longest diagonal of the parallelogram is ( \sqrt{292} ).

By signing up, you agree to our Terms of Service and Privacy Policy

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.

- Is a rectangle a parallelogram always, sometimes or never?
- A parallelogram has sides with lengths of #16 # and #9 #. If the parallelogram's area is #144 #, what is the length of its longest diagonal?
- A parallelogram has sides with lengths of #12 # and #8 #. If the parallelogram's area is #72 #, what is the length of its longest diagonal?
- Two rhombuses have sides with lengths of #4 #. If one rhombus has a corner with an angle of #(pi)/6 # and the other has a corner with an angle of #(3pi)/4 #, what is the difference between the areas of the rhombuses?
- Two rhombuses have sides with lengths of #11 #. If one rhombus has a corner with an angle of #pi/12 # and the other has a corner with an angle of #(7pi)/8 #, what is the difference between the areas of the rhombuses?

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7