What are the three dimensions of a box when it has a volume of #12m^2#, and one side has length #2#, another has length #L#, and a third has length #L+1#?

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Answer 1 · 2018-03-18T06:20:53

The dimensions are #2m, 2m and 3m#

The Volume of a a box (assumed to be rectangular) is found from the formula;

# l xxb xxh =V#

Substitute the given values into the formula to find #L#

#2(L)(L+1) =12#

#2L(L+1)=12" "larr div 2# and multiply out the bracket

#L^2+L = 6" "larr# make a quadratic equal to #0#

#L^2 +L -6=0" "larr# factorise

#(L+3)(L-2)=0#

Set each factor equal to #0#

#L-2 = 0" "rarr L = 2#

#L+3=0" "rarr L=-3" "#(reject as the length of a side)

Now you have #L#, the unknown sides are #2and 3 " "#(from #L+1#)

The dimensions are therefore #2,2 and 3#

Check: #V = 2 xx2xx3 = 12#