Two opposite sides of a parallelogram each have a length of #4 #. If one corner of the parallelogram has an angle of #(5 pi)/6 # and the parallelogram's area is #56 #, how long are the other two sides?

Answer 1

The other length is 28

Notice that the wording of the question is such that we can chose which of the opposite sides we may assign the length of 4.

#color(blue)("Declaring all the relationships")#

Given than #angle ADC = 5/6pi =>angle EDC=angle DAB=1/6pi->30^o#

Let #angle AFB = pi/2#

Then #Delta AFB# is half of an equilateral triangle

Thus #angle ABF = 3/6pi#

Assign the length of 4 to AB

Let the length #AD = L#

Given that the area =56

Known: area#=hL# where #h->FB#

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#color(blue)(" Calculating the other length")#

Thus we have: #area=Lh=56#

Known: #h=4sin(1/6pi)#

#=>Lxx4sin(1/6pi)=56#

But #sin(1/6pi)=1/2# giving

#" "(4L)/2=56#

#color(blue)(=>L=(2xx56)/4 =28 )#
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Answer 2

Avery Allen

The length of the other two sides of the parallelogram is 14.

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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.