SOLUTION: A piece of sheet metal, w = 24 inches wide, is bent to form the gutter shown in the illustration. If the cross-sectional area is 54 square inches, find the depth of the gutter. (En

Click here to see ALL problems on Probability-and-statistics

Question 988980: A piece of sheet metal, w = 24 inches wide, is bent to form the gutter shown in the illustration. If the cross-sectional area is 54 square inches, find the depth of the gutter. (Enter your answers as a comma-separated list.)
The picture is on this link:
https://www.webassign.net/gfcolalg/1-4-10.gif
Answer by macston(5194) (Show Source):
You can put this solution on YOUR website!
.
W=width; H=height
.
W+2H=24in
W=24in-2H
.
Area=WH
54in^2=WH
54in^2=(24-2H)(H)
54in^2=24H-2H^2
2H^2-24H+54=0
H^2-12H+27=0
(H-3)(H-9)=0
H-3=0 OR H-9=0
H=3 OR H=9
W=24-2H
W=24-2(3) OR W=24-2(9)
W=24-6 or W=24-18
W=18 or W=6
If width=18, height=3; if width=6, height=9
.
The picture can not match the problem. The 24 inch wide metal cannot be formed to have a width=2x and height=x AND have a cross sectional area of 54 in^2