Use the surface area formula of a rectangular prism to find the width. (I have changed it to use the same terms given in the problem).
A
=
2
(
d
w
+
h
w
+
h
d
)
Because of the given information, it is known that:
A
=
208
h
=
8
d
=
6
The width is not know, so let it keep it's variable
w
. But substitute the other values into the equation:
A
=
2
(
d
w
+
h
w
+
h
d
)
208
=
2
[
6
w
+
8
w
+
(
8
)
(
6
)
]
208
=
2
(
14
w
+
48
)
Use the distributive property to solve the right side of the equal sign:
208
=
2
(
14
w
+
48
)
208
=
28
w
+
96
112
=
28
w
112
28
=
w
4
=
w
The width is
4
.
