Question

the perimetr of a triangle is 30 units. the length of the sides form an arithmetic sequence. if each length is a whole number determine all possible sets of lengths of the sides of the triangle

Answer 1

Hello,

Lets' assume a the side and r the commun added number

sides: a,a+r,a+2r
p=a+a+r+a+2r=3a+3r

==>a+r=10
Side 0 doesn't exist

a=1,r=9==>1,10,19
a=2,r=8==>2,10,18
a=3,r=7==>3,10,17
a=4,r=6==>4,10,16
a=5,r=5==>5,10,15
a=6,r=4==>6,10,14
a=7,r=3==>7,10,13
a=8,r=2==>8,10,12
a=9,r=1==>9,10,11