The pool

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

Correct result:

a =  10 m
b =  7 m

Solution:

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

Our quadratic equation calculator calculates it.

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

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