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If the green square has area 4, what is the area of the blue square?

 

 Jul 1, 2020
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The green square has area 4, that means its sides are 2 

Therefore, its diagonal length is 2•sqrt(2) 

 

The entire dotted line is 7•sqrt(2) and the piece of it in the green square is 2•sqrt(2)

Therefore, the piece of dotted line in the blue square is 5•sqrt(2) 

 

The section of dotted line in the green square is its diagonal 

and the diagonal of a square runs at a 45o angle 

Since it's a straight line, it is also running at a 45o angle once it enters the blue square 

 

The 45o line in the blue square creates an isoceles triangle out of the corner  

The hypotenuse of that triangle (the dotted line) is 5•sqrt(2) 

Therefore the legs of the triangle are 5 

 

The side of the green triangle is 2, and add the leg of the blue triangle 5

Therefore the entire length of the side of the blue square is 7 

Which makes the area of the blue square A = 72 = 49  

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 Jul 1, 2020

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