Find geometric mean and hence #w# in the following figure?

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1 Answer
Mar 4, 2017

#w=6# and figure represents geometric mean between #12# and #27#, which is #18#.

Explanation:

You have not stated the numbers or unknowns, whose geometric mean you seek to find.

However, image enclosed by you indicates that the geometric mean between #2w# and #4w+3# is #3w#, as
enter image source here
in such a figure geometric mean between #x# and #y# is #h#

or #x/h=h/y# i.e. #x xx y = h^2#. Hence, in given problem

#2wxx(4w+3)=(3w)^2#

or #8w^2+6w=9w^2#

or #w^2-6w=0#

or #w(w-6)=0# i.e. #w=0# or #w=6#

As we are dealing with a geometric figure and #w# cannot be zero (as this leads to #x=0# and #h=0#), the answer is

#w=6# and figure represents geometric mean between #12# and #27#, which is #18#.