Question

A rectangular folder has an area of 54 square inches and a perimeter of 30 inches. what are the dimensions of the folder?

Answer 1

A=LW
P=2(L+W)

54=LW
30=2(L+W)
15=L+W
minus W both sides
15-W=L
sub 15-W for L

54=(15-W)W

54=15W-W^2

times -1 both sides

-54=W^2-15W

add 54 both sides

0=W^2-15W+54

factor

what 2 numbers multiply to get 54 and add to get -15

-9 and -6

0=(W-9)(W-6)
set to zero
w-9=0
w=9
w-6=0
w=6

15-W=L
15-9=6
15-6=9

the dimentions are 6 inches by 8 inches

Answer 2

9 by 6. 9 • 6 = 54 and 6 + 6 + 9 + 9 = 30. Hope I helped! :)