What methods should I use ?

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Answer 1 · 2017-08-28T07:53:31

#390 cm^3#

First work with the surface area information. Remember there are 6 sides (all numbers in cm):

#2{6(2x+3)+6x+x(2x+3)}=346#

#{12x+18+6x+2x^2+3x}=173#

#2x^2+21x+18=173#

#2x^2+21x-155=0#

And now I'll use the Pythagorean Formula

# x = (-b \pm sqrt(b^2-4ac)) / (2a) #

# x = (-21 \pm sqrt(21^2-4(2)(-155))) / (2(2)) #

# x = (-21 \pm sqrt(441+1240)) / 4 #

# x = (-21 \pm sqrt(1681)) / 4 #

# x = (-21 \pm 41) / 4 #

I'll only consider the positive value since we are dealing with a length:

#x=(-21+41)/4=20/4=5#

We can now find the length of all the sides:

The volume of the box can be found with:

#V=LHD=13xx6xx5=390 cm^3#