Swimming pool

The pool shape of a cuboid is 299 m³, full of water. Determine the dimensions of its bottom if the water depth is 282 cm, and one bottom dimension is 4.7 m greater than the second.

Correct answer:

a =  8.21 m
b =  12.91 m

Step-by-step explanation:

$$\begin{gathered} V=abc=299m^3 \\ c=282cm=2.82m \\ 299=a(a+4.7).2.82 \\ {a}^2+4.7a-106.028=0 \\ p=1;q=4.7;r=-106.028 \\ D=q^2-4pr=4.7^2-4\cdot 1\cdot (-106.028)=446.2034751773 \\ D>0 \\ {a}_{1,2}=\frac{-q\pm \sqrt{D}}{2p}=\frac{-4.7\pm \sqrt{446.2}}{2} \\ {a}_{1,2}=-2.35\pm 10.561764 \\ {a}_1=8.211764474 \\ {a}_2=-12.911764474 \\ \text{ Factored form of the equation: } \\ (a-8.211764474)(a+12.911764474)=0 \\ a>0 \\ a=8.21\text{m} \end{gathered}$$

$b=a+4.7=12.91\text{m}$

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