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A parallelogram has sides with lengths of #9 # and #8 #. If the parallelogram's area is #63 #, what is the length of its longest diagonal?

Answer 1

Theodore Abad

#=15.35#

Area of Parallelogram #=63=ab sintheta# where #a=9# and #b=8# or #63=9times8timessintheta# or

#sin theta=63/72# or #sin theta=7/8# or #theta=sin^-1(7/8)# or #theta=61#

To find the longer diagonal #=y=?#

we have to get the supplementary of the angle #35.7#

So we have Angle #180-61=129#

Using the Law of Cosine we can write #y^2=9^2+8^2-2times9times8cos(129)#

#=81+64-2times9times8(-0.63)#

#=145+90.72#

#=235.72# or #y=sqrt235.72#

#=15.35#

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Answer 2

Noah Atkinson

The length of the longest diagonal of the parallelogram is 17 units.

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Answer from HIX Tutor

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.