Swimming pool

The pool shape of a cuboid is 237 m³, full of water. Determine the dimensions of its bottom if the water depth is 199 cm, and one bottom dimension is 4.8 m greater than the second.

Final Answer:

a =  8.7739 m
b =  13.5739 m

Step-by-step explanation:

$$\begin{gathered} V=237{\text{m}}^3 \\ c=199\text{cm}\to \text{m}=199:100\text{m}=1.99\text{m} \\ V=abc=237 \\ 237=a(a+4.8)\cdot c \\ 237=a(a+4.8)\cdot 1.99 \\ -1.99a^2-9.552a+237=0 \\ 1.99a^2+9.552a-237=0 \\ p=1.99;q=9.552;r=-237 \\ D=q^2-4pr=9.552^2-4\cdot 1.99\cdot (-237)=1977.760704 \\ D>0 \\ {a}_{1,2}=\frac{-q\pm \sqrt{D}}{2p}=\frac{-9.55\pm \sqrt{1977.76}}{3.98} \\ {a}_{1,2}=-2.4\pm 11.173875 \\ {a}_1=8.773874771 \\ {a}_2=-13.573874771 \\ a>0 \\ a=a_1=8.7739=8.7739\text{m} \end{gathered}$$

Our quadratic equation calculator calculates it.

$$\begin{gathered} b=a+4.8=8.7739+4.8\doteq 13.5739\text{m} \\ \text{ Verifying Solution: } \\ {V}_2=a\cdot b\cdot c=8.7739\cdot 13.5739\cdot 1.99=237{\text{m}}^3 \end{gathered}$$

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