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.

Correct answer:

a =  18

Step-by-step explanation:

$$\begin{gathered} S_1=S_2 \\ {a}^2=(a+9)(a-6) \\ {a}^2=a^2+9a-6a-9\cdot 6 \\ 3a=9\cdot 6 \\ a=9\cdot 6\mathrm{/}3=18 \\ {S}_1=a^2=18^2=324 \\ {S}_2=(a+9)\cdot (a-6)=(18+9)\cdot (18-6)=324 \end{gathered}$$

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