Question 1201827
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I agree with the tutor @greenestamps
The problem seems to lack instructions as to exactly how the squares are connected.


Here is an interactive GeoGebra diagram where you can slide the smaller square up and down. 
Move the red point to do so.
<a href = "https://www.geogebra.org/m/krtatgey">https://www.geogebra.org/m/krtatgey</a>
Click the curved arrow if the diagram doesn't show up. That should refresh the page.


The GeoGebra app will compute the perimeter to give approximate values as a result.
The diagram is to scale.


If the smaller square is fully attached to the larger square, i.e. no "spillover", then the perimeter is {{{26*sqrt(3)}}} as the other tutors mention (the tutor @mananth doesn't mention it directly, but you can arrive at this figure after adding up the terms they wrote).


However, if some piece of the smaller square is not attached to the larger, then the perimeter will exceed {{{26*sqrt(3)}}}
It will be within the interval of {{{26*sqrt(3) < perimeter < 32*sqrt(3)}}}


Here's where I'm getting the {{{32*sqrt(3)}}}
First compute the perimeter of each square separately
perimeter of larger square = {{{4*side = 4*5*sqrt(3) = 20*sqrt(3)}}}
perimeter of smaller square = {{{4*side = 4*3*sqrt(3) = 12*sqrt(3)}}}
Then add up the perimeters {{{perimeterA+perimeterB = 20*sqrt(3)+12*sqrt(3) = 32*sqrt(3)}}}
This is the largest possible perimeter of the complex shape. 
If we slide the red point up as far as you can go, we'll have two squares as separate "islands" so to speak, and it should help visualize why I just added the perimeters.


Also, the red shared wall is subtracted twice from that total sum to arrive at the perimeter of the complex shape.
This because this shared wall is included in the calculation of perimeterA+perimeterB, but clearly the shared wall is interior (not exterior). We subtract off 2 copies because there are 2 squares.


Footnotes:
{{{sqrt(3) = 1.7321}}}
{{{5*sqrt(3) = 8.6603}}}
{{{3*sqrt(3) = 5.1962}}}
{{{26*sqrt(3) = 45.0333}}}
{{{32*sqrt(3) = 55.4256}}}
Each decimal value is approximate.
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