Rectangle - area, perimeter

The area of a rectangular field is equal to 300 square meters. Its perimeter is equal to 70 meters. Find the length and width of this rectangle.

Correct answer:

a =  20 m
b =  15 m

Step-by-step explanation:

$$\begin{gathered} S=300{\text{m}}^2 \\ p=70\text{m} \\ S=ab \\ p=2(a+b) \\ 300=ab \\ 35=a+b \\ a(35-a)=300 \\ -a^2+35a-300=0 \\ {a}^2-35a+300=0 \\ p=1;q=-35;r=300 \\ D=q^2-4pr=35^2-4\cdot 1\cdot 300=25 \\ D>0 \\ {a}_{1,2}=\frac{-q\pm \sqrt{D}}{2p}=\frac{35\pm \sqrt{25}}{2} \\ {a}_{1,2}=\frac{35\pm 5}{2} \\ {a}_{1,2}=17.5\pm 2.5 \\ {a}_1=20 \\ {a}_2=15 \\ a=a_1=20=20\text{m} \end{gathered}$$

Our quadratic equation calculator calculates it.

$$\begin{gathered} b=a_2 \\ b=35-a=35-20=15\text{m} \end{gathered}$$

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