hey this is presh talwalkar
we'll start out with the square
from the bottom left corner of the
square i'll draw a line segment to the
interior with the length of 12.
from the endpoint of this line segment
i'll construct a perpendicular going up
and to the left with the length of three
from the endpoint of this line segment
i'll construct another perpendicular
that connects to the upper right hand
corner of the square
and this line segment has a length of
nine
the question is
from the given information
what is x the length of the square's
side
can you figure it out
give this problem a try and when you're
ready keep watching the video for the
solution
so before i present the approach that
eventually led me to the answer i want
to go over some of the approaches that
did not work for me
i first considered the right triangles
in the interior of the square
while i could solve for the areas of
these triangles and the hypotenuses of
these triangles
this didn't lead me directly to the
length of the square side
i then tried to work out the problem
using coordinate geometry
but in spite of trying a few equations i
still wasn't able to solve for x
so then it struck me in the third
approach i took to this problem
i imagine focusing on just the inside
line segments
in the interior of the square
i wanted to figure out the distance from
end to end
so i considered what would happen if i
rotated the figure so it'd be easier to
analyze
then it struck me
i connected the endpoints of these line
segments
and then i realize we basically have one
large right triangle
i can move the length of nine down to
form one leg of this right triangle
and then i can move the length of three
over to create another leg of this right
triangle
so we can then solve for the distance
using the pythagorean theorem
we have one leg of the triangle that's
12 plus 9 or 21
and another leg which is 3.
so the length of the hypotenuse is the
square root of 21 squared plus 3 squared
this becomes the square root of 450
which is also equal to the square root
of 225 times 2 which then becomes 15
times the square root of 2.
so now let's take this information and
get back to the original diagram
we'll recreate our line segments on
interior of the square and then we'll
rotate them
so that we have the distance
from one corner of the square to the
other corner of the square
we know the diagonal of the square is 15
square root of 2 that's what we
calculated
and now we also know that the diagonal
square is x times the square root of 2.
this is because the diagonal of the
square is the hypotenuse of a right
triangle with two legs that are each x
so we can set 15 square root of 2 to be
x times the square root of 2 and we can
solve that x is equal to 15.
and that's our answer
so it took a little bit of work to
figure out what the length of the square
side is
and sometimes in these problems you have
to approach them in more than one
attempt
in this problem it took me three
attempts before i could solve it
did you figure out this problem and did
you come up with another solution
thanks for watching this video please
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