Square

Suppose the square's sides' length decreases by a 25% decrease in the content area of 28 cm². Determine the side length of the original square.

Correct result:

a =  8 cm

Solution:

$$\begin{gathered} a^2-((1-25\mathrm{/}100)a{)}^2=28 \\ 0.4375a^2-28=0 \\ p=0.4375;q=0;r=-28 \\ D=q^2-4pr=0^2-4\cdot 0.4375\cdot (-28)=49 \\ D>0 \\ {a}_{1,2}={\displaystyle \frac{-q\pm \sqrt{D}}{2p}}={\displaystyle \frac{\pm \sqrt{49}}{0.875}} \\ {a}_{1,2}={\displaystyle \frac{\pm 7}{0.875}} \\ {a}_{1,2}=\pm 8 \\ {a}_1=8 \\ {a}_2=-8 \\ \text{ Factored form of the equation: } \\ 0.4375(a-8)(a+8)=0 \\ a=a_1=8=8\text{ cm} \end{gathered}$$

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