Question

Daniel has 8 wire panels that he will use as the side of a new cage for his guinea pig, oscar. Each panel is 1 foot long
a) If he make the length of the base of the cage 3 feets and its total area will be 3 square feet,what will be width of the base of the cage be? Show work
b) If he instated made all of side of the base 2 feet long, would Oscar have more room?.Shoe your work.

Answer 1

Cage width will be 1 foot and length, 3 feet. The perimeter will be 8 feet long, 2*1 + 2*3 = 8.

From Mathematica:

Maximize [ { L*w, 2*L + 2*w == 8 }, { L, w } ]
-> { 4, { L -> 2, w -> 2 } }

Answer 2

a

l*w=A,
3ft=length
1ft= width
3*1= total area 3 ft

b

l*w= A
if all sides of the base were 2 ft
2ft *2 ft= 4ft
more room than 3 ft