One side 2

One side of the rectangle is three times larger, and the other is 4 cm smaller than the side of the square. Find the area of the square if more than the area of the rectangle by 10 cm².

Final Answer:

A =  25 cm²

Step-by-step explanation:

$$\begin{gathered} a=3x \\ b=x-4 \\ S=ab+10=x\cdot x \\ 3x\cdot (x-4)+10=x\cdot x \\ 3x\cdot (x-4)+10=x\cdot x \\ 2x^2-12x+10=0 \\ 2...\text{ prime number} \\ 12=2^2\cdot 3 \\ 10=2\cdot 5 \\ \text{GCD}(2,12,10)=2 \\ {x}^2-6x+5=0 \\ a=1;b=-6;c=5 \\ D=b^2-4ac=6^2-4\cdot 1\cdot 5=16 \\ D>0 \\ {x}_{1,2}=\frac{-b\pm \sqrt{D}}{2a}=\frac{6\pm \sqrt{16}}{2} \\ {x}_{1,2}=\frac{6\pm 4}{2} \\ {x}_{1,2}=3\pm 2 \\ {x}_1=5 \\ {x}_2=1 \\ x=x_1=5\text{cm} \\ A=x\cdot x=5\cdot 5=25=25{\text{cm}}^2 \\ \text{ Verifying Solution: } \\ a=3\cdot x=3\cdot 5=15\text{cm} \\ b=x-4=5-4=1\text{cm} \\ {S}_1=a\cdot b=15\cdot 1=15{\text{cm}}^2 \end{gathered}$$

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