Rectangle - sides

A rectangle has an area 266 cm². The length of the shorter side is 5 cm fewer than the length of the longer side. What is the perimeter of a rectangle?

Correct answer:

x =  66 cm

Step-by-step explanation:

$$\begin{gathered} ab=266 \\ b=a+5 \\ a(a+5)=266 \\ {a}^2+5a-266=0 \\ {a}^2+5a-266=0 \\ p=1;q=5;r=-266 \\ D=q^2-4pr=5^2-4\cdot 1\cdot (-266)=1089 \\ D>0 \\ {a}_{1,2}=\frac{-q\pm \sqrt{D}}{2p}=\frac{-5\pm \sqrt{1089}}{2} \\ {a}_{1,2}=\frac{-5\pm 33}{2} \\ {a}_{1,2}=-2.5\pm 16.5 \\ {a}_1=14 \\ {a}_2=-19 \\ \text{ Factored form of the equation: } \\ (a-14)(a+19)=0 \\ a=14 \\ b=19 \\ o=2(a+b)=66\text{cm} \end{gathered}$$

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