Question 134501
Let L=Lenth, B=Width
given:
Perimeter=2L+2B=72
L+B=36....EQN 1
Also B+6:L+6=7:9
in a ratio product of mid terms = product of extreme terms
7(L+6)=9(B+6)
7L+42=9B+54
7L-9B=54-42=12
..
7L-9B=12
9L+9B=324 FROM EQN 1 (MUTIPLIED BY 9)
Adding 16L=336
L=336/16=21
B=36-21=15

So answer : Length = 21 and width=15
Verification

add 6 to both
L:B=21+6:15+6
L:B=27:21
L:B=9:7
Okay