The width

The width of a rectangular garden is 4 m less than the length. If the area of a rectangular garden is 96 square meters, what is the garden's dimension?

Correct answer:

a =  8 m
b =  12 m

Step-by-step explanation:

$$\begin{gathered} S=96 \\ S=ab \\ a=b-4 \\ S=a\cdot (a+4) \\ 96=a\cdot (a+4) \\ -a^2-4a+96=0 \\ {a}^2+4a-96=0 \\ p=1;q=4;r=-96 \\ D=q^2-4pr=4^2-4\cdot 1\cdot (-96)=400 \\ D>0 \\ {a}_{1,2}=\frac{-q\pm \sqrt{D}}{2p}=\frac{-4\pm \sqrt{400}}{2} \\ {a}_{1,2}=\frac{-4\pm 20}{2} \\ {a}_{1,2}=-2\pm 10 \\ {a}_1=8 \\ {a}_2=-12 \\ a=a_1=8=8\text{m} \end{gathered}$$

Our quadratic equation calculator calculates it.

$b=a+4=8+4=12\text{m}$

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