Answer:
Step-by-step explanation: Explanation:
If
L
,
H
and
W
represent the length, height and width of the prism, then the volume of the rectangular prism is :
V
=
L
.
H
.
W
............. (1)
Given :
V
=
x
3
+
11
x
2
+
20
x
−
32
;
............... (2)
W
=
(
x
−
1
)
;
 Â
H
=
(
x
+
8
)
.
Let
L
=
(
x
+
l
0
)
be the expression for the length, then the RHS of equation (1) becomes
L
.
H
.
W
=
(
x
−
l
0
)
(
x
+
8
)
(
x
−
1
)
,
 Â
 Â
 Â
 Â
=
(
x
+
l
0
)
(
x
2
+
7
x
−
8
)
 Â
 Â
 Â
 Â
=
(
x
+
l
0
)
(
x
2
+
7
x
−
8
)
 Â
 Â
 Â
 Â
=
x
3
+
(
7
+
l
0
)
x
2
+
(
7
l
0
−
8
)
x
−
8
l
0
..... (3)
Comparing this to the LHS of equation (1), we get the following set of equations to solve for
l
0
,
7
+
l
0
=
11
;
 Â
7
l
0
−
8
=
20
;
 Â
8
l
0
=
32
;
l
0
=
4
Therefore
L
=
(
x
+
4
)
