Width and length

For a particular rectangle, twice the width is 1 meter longer than the length. The area of the rectangle is 153 square meters. What is the perimeter of the rectangle?

Final Answer:

p =  52 m

Step-by-step explanation:

$$\begin{gathered} 2a=1+b \\ A=153{\text{m}}^2 \\ A=ab \\ A=a\cdot (2\cdot a-1) \\ 153=a\cdot (2\cdot a-1) \\ -2a^2+a+153=0 \\ 2a^2-a-153=0 \\ p=2;q=-1;r=-153 \\ D=q^2-4pr=1^2-4\cdot 2\cdot (-153)=1225 \\ D>0 \\ {a}_{1,2}=\frac{-q\pm \sqrt{D}}{2p}=\frac{1\pm \sqrt{1225}}{4} \\ {a}_{1,2}=\frac{1\pm 35}{4} \\ {a}_{1,2}=0.25\pm 8.75 \\ {a}_1=9 \\ {a}_2=-8.5 \\ a=a_1=9\text{m} \\ b=2\cdot a-1=2\cdot 9-1=17\text{m} \\ p=2\cdot (a+b)=2\cdot (9+17)=52\text{m} \end{gathered}$$

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