# Water reservoir

The cuboid reservoir contains 1900 hectoliters of water and the water height is 2.5 m. Determine the dimensions of the bottom where one dimension is 3.2 m longer than the second one.

Correct result:

a =  7.26 m
b =  10.46 m

#### Solution:

$V = abc = 1900 \ hl = 190 \ m^3 \ \\ 190 = 2.5 ab \ \\ ab = 76 \ \\ b = 3.2+a \ \\ \ \\ a(3.2+a) = 76 \ \\ a^2 + 3.2 a - 76 = 0 \ \\ \ \\ x_{1,2} = \dfrac{ -b \pm \sqrt{ D } }{ 2a } = \dfrac{ -3.2 \pm \sqrt{ 314.24 } }{ 2 } \ \\ x_{1,2} = -1.6 \pm 8.86340792246 \ \\ x_{1} = 7.26340792246 \ \\ x_{2} = -10.4634079225 \ \\ \ \\ a = 7.26 \ \text{m}$

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