A parallelogram has sides with lengths of #24 # and #9 #. If the parallelogram's area is #54 #, what is the length of its longest diagonal?

Answer 1

#D=32,8#

The area is #Area=24*9*sintheta=54# we can deduce #sintheta=54/(24*9)=1/4# we have to solution to this goniometric equation #theta_1=arcsin(1/4)~~14,48°# and #theta_2=pi-arcsin(1/4)~~165,52°# the first opposite the shortest diagonal and the second opposite the longest diagonal whise length is #D=root2(24^2+9^2-2*24*9*costheta_2)# or equivalently #D=root2(24^2+9^2+2*24*9*costheta_1)# #D=root2(576+81+418,28)~~32,8#

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

Answer 2

Wyatt Anderson

The length of the longest diagonal of the parallelogram is 30 units.

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

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.