Question

A company makes concrete paving stones in different sizes. Each stone has a volume of 360 cubic inches and a height of 4 inches. How many different paving stones could be made if any whole number length and width?

Answer 1

v=lwh
given
v=360
h=4
360=lw4
divide both sides by 4
90=lw
k, factor 90
90=1*2*3*3*5
so the possible combos are
1*90
2*45
3*30
5*18
6*15
9*10
then they just reverse
that was 6 ways
if we say that a 9 by 10 paving stone is the same as a 10 by 9 paving stone then there are 6 different paving stones can be made

if we say that a 9 by 10 paving stone is different from a 10 by 9 paving stone then there are 6*2 or 12 different paving stones can be made