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A parallelogram has sides with lengths of #9 # and #8 #. If the parallelogram's area is #32 #, what is the length of its longest diagonal?

Answer 1

Caroline Aucoin

It is #16.55#.

Consider the image. From the initial data we have

#A=9, B=8#, the area is #32#.
We know that the area is #A*h# so we have

#A*h=32# and then

#h=32/9=3.\bar{5}#

For the longest diagonal we need to know #C# that is

#C=sqrt(B^2-h^2)=sqrt(8^2-3.\bar{5}^2)\approx7.166#

Finally, the diagonal is

#D=sqrt((A+C)^2+h^2)=sqrt((9+7.166)^2+3.\bar{5}^2)#

#=sqrt(16.166^2+3.\bar{5}^2)\approx16.55#.

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Answer 2

Autumn Armstrong

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

Longest diagonal length = √(a^2 + b^2 + 2ab)

Where 'a' and 'b' are the lengths of the sides of the parallelogram.

Given: a = 9 b = 8

Using the formula: Longest diagonal length = √(9^2 + 8^2 + 298)

Longest diagonal length = √(81 + 64 + 144)

Longest diagonal length = √289

Longest diagonal length ≈ 17

So, the length of the longest diagonal of the parallelogram is approximately 17 units.

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Answer from HIX Tutor

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