SOLUTION: A square with a side equal to ( 2x)m is made up of four smaller equal squares One of the squares is removed and the remaining shaded area is 75m squared . Calculate the value of

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Question 1090439: A square with a side equal to ( 2x)m is made up of four smaller equal squares
One of the squares is removed and the remaining shaded area is 75m squared . Calculate the value of x

Found 2 solutions by Boreal, KMST:
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
Drawing this helps
Area of whole thing is 4x^2 m^2
1/4 is removed
3x m^2 remains
that equals 75 m^2
therefore x^2=75/3=25 m^2
x=5 m

Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
If the side of the large square measures 2x m ,
the area of the large square in m%5E2 is
%282x%29%5E2=4x%5E2 , and
the area in m%5E2 of each of the four smaller squares is
4x%5E2%2F4=x%5E2 .

After one of the small squares is removed, a figure made up of
4-1=3 of the small squares is remaining.
It's area in k%5E2 is 3x%5E2=75 , so
x%5E2=75%2F3 ,
x%5E2=25 .
That means that x=sqrt%2825%29=highlight%285%29 .