Q is the midpoint of GH¯¯¯¯¯¯ , GQ=2x+3, and GH=5x−5 . What is the length of GQ¯¯¯¯¯ ?

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Answer 1 · 2016-12-19T05:44:03

#GQ=25#

As #Q# is the midpoint of #GH#, we have #GQ=QH# and

#GH=GQ+QH=2xxGQ#

Now as #GQ=2x+3#, and #GH=5x−5#, we have

#5x-5=2xx(2x+3)#

or #5x-5=4x+6#

or #5x-4x=6+5#

i.e. #x=11#

Hence, #GQ=2xx11+3=22+3=25#