A parallelogram has sides with lengths of #16 # and #8 #. If the parallelogram's area is #24 #, what is the length of its longest diagonal?

Question

A parallelogram has sides with lengths of #16  # and #8  #.  If the parallelogram's area is #24  #, what is the length of its longest diagonal?

Savannah Aguilar · Accepted Answer

#23.905#

Area of parallelogram #=BxxH#
#24 =16xxH#, #=> H=3/2=1.5#

#A=sqrt(8^2-H^2)#
#A=sqrt(8^2-1.5^2) = 7.858#

The length of the longest diagonal :

#D=sqrt((16+A)^2+H^2)#
#=sqrt((16+7.858)^2+1.5^2)#
#=23.905#

Ella Armstrong · Answer

undefined 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 16 and 8, and the area is given as 24. Using the formula for the area of a parallelogram (Area = base * height), we can find the height of the parallelogram.

Area = base * height
24 = 16 * height
height = 24/16 = 1.5

Now, using the formula for the longest diagonal:

Diagonal = √(16^2 + 8^2 + 2 * 16 * 8 * cos(180°))

= √(256 + 64 + 256 * (-1))

= √(320 - 256)

= √64

= 8

So, the length of the longest diagonal of the parallelogram is 8.

Autumn Armstrong · Answer

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

$$ \text{Area} = \text{base} \times \text{height} $$

Given that the parallelogram's area is 24 and one of its sides is 16 units, we can solve for the height:

$$ 24 = 16 \times \text{height} $$

$$ \text{height} = \frac{24}{16} $$

$$ \text{height} = 1.5 $$

Since the height of the parallelogram is 1.5 units, and the other side is 8 units, we have formed a right triangle with the diagonal as the hypotenuse. Using the Pythagorean theorem, we can find the length of the longest diagonal $ d $:

$$ d^2 = 8^2 + 1.5^2 $$

$$ d^2 = 64 + 2.25 $$

$$ d^2 = 66.25 $$

$$ d = \sqrt{66.25} $$

$$ d \approx 8.13 $$

Therefore, the length of the longest diagonal of the parallelogram is approximately 8.13 units.