Question 255051
A rectangle has an area of 120 sq. cm.. Its length and width are whole numbers. What are the possibilities for the two numbers? Which possibility gives the smallest perimeter?

find the factors of 120:
120=1*120
120=2*60
120=3*40
120=4*30
120=5*24
120=6*20
120=8*15
120=10*12

perimeter of a rectangle = 2*length + 2 * width = 2 * (length + width)

perimeters of above factorizations:
2*(1+120)=2*121=142
2*(2+60)=2*62=124
2*(3+40)=2*43=86
2*(4+30)=2*34=68
2*(5+24)=2*29=58
2*(6+20)=2*26=52
2*(8+15)=2*23=46
2*(10+12)=2*22=44

the largest factors, 10 and 12 give smallest perimeter which is 44