Answer:
length = 20 meters
width = 66 meters
Explanation:
P = perimeter. l = length. w=width
P = 2l + 2w ==> perimeter formula
Consecutive integers have a difference of 2 ( 4 - 2 = 2 )
Hence, the width(w) in terms of length(l) is:
w = 3 * (l + 2)
w = 3l + 3*2 ==> distribute 3 to l and 2
w = 3l + 6 ==> simplify
P = 2l + 2(3l + 6) ==> substitute w=3l + 6 into the equation P = 2l + 2w
P = 2l + 2*3l + 2*6 ==> distribute 2 to 3l and 6
P = 2l + 6l + 12
P = 8l + 12
172 = 8l + 12 ==> substitute 172 for P since the perimeter is 172 meters
160 = 8l ==> subtract 12 on both sides
l = 20 ==> divide both sides by 8
length = 20 meters
Now solve for the width:
w = 3(20) + 6 ==> substitute l=20 in w = 3l + 6
w = 60 + 6 ==> simplify
w = 66
width = 66 meters