Area and perimeter of rectangle

The content area of the rectangle is 3000 cm², one dimension is 10 cm larger than the other. Determine the perimeter of the rectangle.

Correct answer:

o =  220 cm

Step-by-step explanation:

$$\begin{gathered} 3000=ab \\ a=b+10 \\ 3000=b\ast (b+10) \\ 3000=b\cdot (b+10) \\ -b^2-10b+3000=0 \\ {b}^2+10b-3000=0 \\ p=1;q=10;r=-3000 \\ D=q^2-4pr=10^2-4\cdot 1\cdot (-3000)=12100 \\ D>0 \\ {b}_{1,2}={\displaystyle \frac{-q\pm \sqrt{D}}{2p}}={\displaystyle \frac{-10\pm \sqrt{12100}}{2}} \\ {b}_{1,2}={\displaystyle \frac{-10\pm 110}{2}} \\ {b}_{1,2}=-5\pm 55 \\ {b}_1=50 \\ {b}_2=-60 \\ \text{ Factored form of the equation: } \\ (b-50)(b+60)=0 \\ b=b_1=50\text{ cm } \\ a=b+10=50+10=60\text{ cm } \\ o=2\cdot (a+b)=2\cdot (60+50)=220\text{ cm} \end{gathered}$$

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