a)
original rectangle P = 2(w+l)
so
18 = 2(w+l) (1)
new rectangle
doubling width w, so its 2w
tripling length l, so its 3l
46 = 2(2w + 3l) (2)
now you have
18 = 2(w+l) (1)
9 = w + l so w = 9 - l
46 = 2(2w + 3l) (2)
23 = 2w + 3l
substitute w = 9 - l into 23 = 2w + 3l
23 = 2w + 3l
23 = 2(9 - l) + 3l
23 = 18 - 2l + 3 l
23 - 18 = l
5 = l or l = 5
w = 9 - l = 9 - 5 = 4
answer
original rectangle, length = 5 in and width = 4 in
b)new rectangle
length = 3l = 3(5) = 15 in
width = 2w = 2(4) = 8 in
