Find geometric mean and hence w in the following figure?

enter image source here

1 Answer
Shwetank Mauria
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.

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