# Swimming pool

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

Correct result:

a =  8.21 m
b =  12.91 m

#### Solution:

$V = abc = 299 \ m^3 \ \\ c = 282 \ cm = 2.82 \ m \ \\ \ \\ 299 = a(a+4.7). 2.82 \ \\ \ \\ a^2 +4.7a -106.028 =0 \ \\ \ \\ p=1; q=4.7; r=-106.028 \ \\ D = q^2 - 4pr = 4.7^2 - 4\cdot 1 \cdot (-106.028) = 446.203475177 \ \\ D>0 \ \\ \ \\ a_{1,2} = \dfrac{ -q \pm \sqrt{ D } }{ 2p } = \dfrac{ -4.7 \pm \sqrt{ 446.2 } }{ 2 } \ \\ a_{1,2} = -2.35 \pm 10.5617644735 \ \\ a_{1} = 8.21176447353 \ \\ a_{2} = -12.9117644735 \ \\ \ \\ \text{ Factored form of the equation: } \ \\ (a -8.21176447353) (a +12.9117644735) = 0 \ \\ \ \\ a>0 \ \\ a = 8.21 \ \text{m}$

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