Table side calculation

The area of the work surface of the rectangular table is 70 dm², and its perimeter is 34 dm. Determine (in dm) the length of the shorter side of this table.

Final Answer:

a =  7 dm

Step-by-step explanation:

$$\begin{gathered} S=70{\text{dm}}^2 \\ p=34\text{dm} \\ S=ab \\ p=2(a+b) \\ 70=ab \\ 34/2=a+b \\ a(p/2-a)=S \\ a(34/2-a)=70 \\ -a^2+17a-70=0 \\ {a}^2-17a+70=0 \\ p=1;q=-17;r=70 \\ D=q^2-4pr=17^2-4\cdot 1\cdot 70=9 \\ D>0 \\ {a}_{1,2}=\frac{-q\pm \sqrt{D}}{2p}=\frac{17\pm \sqrt{9}}{2} \\ {a}_{1,2}=\frac{17\pm 3}{2} \\ {a}_{1,2}=8.5\pm 1.5 \\ {a}_1=10 \\ {a}_2=7 \\ a=a_2=7=7\text{dm} \end{gathered}$$

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