Arectangle has an area of 32 square feet and a
perimeter of 24 feet. what is the shortest of the side
lengths, in feet, of the rectangle?
f. 1
g. 2
h. 3
j. 4
k. 8

Perimeter=2l+2w
24=2l+2w
2l=24-2w
l=12-w
Area=lw
32=(12-w)w
32=12w-w^2
w^2-12w+32=0
(w-4)(w-8)=0

w-4=0
w=4 ans. l=12-4=8 ans.
w-8=0
w=9 and. l=12-8=4 ans.
Proof:
24=2*8+2*4
24=16+8
24=24
32=8*4
32=32

Whose mistake? can you give more details to what the question is asking?