# Juice box

The juice box has a volume of 200ml with its base is an isosceles triangle with sides a = 4,5cm and a height of 3,4cm. How tall is the box?

Result

h =  26.144 cm

#### Solution:

$V = 200 \ cm^3 \ \\ 1 \ ml = 1 \ cm^3 \ \\ a = 4.5 \ cm \ \\ v = 3.4 \ cm \ \\ S_{ 1 } = a \cdot \ v/2 = 4.5 \cdot \ 3.4/2 = \dfrac{ 153 }{ 20 } = 7.65 \ cm^2 \ \\ h = V/S_{ 1 } = 200/7.65 = \dfrac{ 4000 }{ 153 } \doteq 26.1438 = 26.144 \ \text{ cm }$

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