The pool

The cube-shaped pool has 140 cubic meters of water. Determine the bottom's dimensions if the water's depth is 200 cm and one dimension of the base is 3 m greater than the other. What are the dimensions of the pool bottom?

Correct answer:

a =  10 m
b =  7 m

Step-by-step explanation:

$$\begin{gathered} V=140{\text{m}}^3 \\ h=200\text{cm}\to \text{m}=200:100\text{m}=2\text{m} \\ V=Sh \\ S=V/h=140/2=70{\text{m}}^2 \\ S=ab \\ b=a-3 \\ S=a(a-3) \\ 70=a(a-3) \\ -a^2+3a+70=0 \\ {a}^2-3a-70=0 \\ p=1;q=-3;r=-70 \\ D=q^2-4pr=3^2-4\cdot 1\cdot (-70)=289 \\ D>0 \\ {a}_{1,2}=\frac{-q\pm \sqrt{D}}{2p}=\frac{3\pm \sqrt{289}}{2} \\ {a}_{1,2}=\frac{3\pm 17}{2} \\ {a}_{1,2}=1.5\pm 8.5 \\ {a}_1=10 \\ {a}_2=-7 \\ a=a_1=10=10\text{m} \end{gathered}$$

Our quadratic equation calculator calculates it.

$b=a-3=10-3=7\text{m}$

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