# A parallelogram has sides with lengths of #15 # and #12 #. If the parallelogram's area is #27 #, what is the length of its longest diagonal?

Length of longer diagonal is

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:

Diagonal = √(side1^2 + side2^2 + 2 * side1 * side2 * cos(angle))

In this case, the lengths of the sides are given as 15 and 12, and the area is given as 27. Using the formula for the area of a parallelogram (Area = base * height), we can find the height of the parallelogram.

Area = base * height 27 = 15 * height height = 27/15 = 1.8

Now, using the formula for the longest diagonal:

Diagonal = √(15^2 + 12^2 + 2 * 15 * 12 * cos(180°))

= √(225 + 144 + 360 * (-1))

= √(369 - 360)

= √9

= 3

So, the length of the longest diagonal of the parallelogram is 3.

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.

- If a shape is called a rhombus, then is it automatically also called a kite. why or why not?
- Two rhombuses have sides with lengths of #9 #. If one rhombus has a corner with an angle of #pi/12 # and the other has a corner with an angle of #pi/3 #, what is the difference between the areas of the rhombuses?
- A parallelogram has sides with lengths of #16 # and #9 #. If the parallelogram's area is #120 #, what is the length of its longest diagonal?
- Two opposite sides of a parallelogram have lengths of #3 #. If one corner of the parallelogram has an angle of #pi/12 # and the parallelogram's area is #14 #, how long are the other two sides?
- A parallelogram has sides with lengths of #16 # and #9 #. If the parallelogram's area is #21 #, what is the length of its longest diagonal?

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