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 m3 c=282 cm=2.82 m  299=a(a+4.7).2.82  a2+4.7a106.028=0  p=1;q=4.7;r=106.028 D=q24pr=4.7241(106.028)=446.203475177 D>0  a1,2=q±D2p=4.7±446.22 a1,2=2.35±10.5617644735 a1=8.21176447353 a2=12.9117644735   Factored form of the equation:  (a8.21176447353)(a+12.9117644735)=0  a>0 a=8.21 mV = 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}
b=a+4.7=12.91 m



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