Find b, c and d so that the quadrilateral is a parallelogram with area equal to 80 square units?

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Answer 1 · 2016-11-07T09:56:14

#b=14, c=8, d=18#

To achieve parallelism

#y_C-y_B=y_D-y_A#

#d-b= 2-(-2)#

#d=b+4#

#x_C-x_B=x_D-x_A#

#c-2= 4-(-2)#

#c=2+6=8#

so

#C=(8;b+4)#

Now let #B^', D^', C^'# be the projection of #B,D,C# on the horizontal line passing per A then

#A_(ABCD) = A_(ABB^')+A_(B^'BC C^')-A_(ADD^')-A_(D^'DC C^')#

so

#80=(4*(b+2))/2+((b+2+b+6)*6)/2-(6*4)/2-((4+b+6)*4)/2#

#80=2b+4+6b+24-12-2b-20#

#80=6b-4#

#6b=84#

#b=14#

#d=18#