Answer: x = 12
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Step-by-step explanation:
The hexagon is broken up into 6 congruent or identical equilateral triangles. If we find the area of one triangle, then we multiply by 6 to get the area of the hexagon.
Going in reverse, we divide the hexagon's area by 6 to get the area of one equilateral triangle
We're told the hexagon has an area of
square inches. Divide this by 6 and you should get the result
. So each of the six equilateral triangles has area of
square inches.
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Each triangle has a base of
and a height of

The x/12 and x/6 are exponents.
Let
and
be the base and height respectively.
Also, let
be the area of the triangle
We can then solve for x like so:

Since the bases are equal to 3, this means the exponents must be equal as well (for both sides overall to be equal)
3/2 = x/8
3*8 = 2*x ... cross multiply
24 = 2x
2x = 24
x = 24/2
x = 12