# Square vs rectangle

Square and rectangle have the same area contents. The length of the rectangle is 9 greater and width 6 less than side of the square. Calculate the side of a square.

Result

a =  18

#### Solution:

$S_{1}=S_{2} \ \\ a^2=(a+9)(a-6) \ \\ a^2=a^2+9a-6a-9 \cdot \ 6 \ \\ 3a=9 \cdot \ 6=18 \ \\ a=9 \cdot \ 6/3=18 \ \\ S_{1}=a^2=18^2=324 \ \\ S_{2}=(a+9) \cdot \ (a-6)=(18+9) \cdot \ (18-6)=324$

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