Answer:
x = 5.
Step-by-step explanation:
The area of a rectangle can be determined by the following formula.
A
=
l
⋅
w
l stands for length or the longer side.
w stands for width or the shorter side.
Now, we can plug the values we are given into the equation.
A
=
(
x
−
2
)
⋅
(
x
+
8
)
The easiest way to multiply is to follow the acronym FOIL , which stands for First Outside Inside Last, and dictates the order in which you multiply these terms.
A
=
x
2
+
8
x
−
2
x
−16
=
x
2
+
6
x
−
16
Now, we can plug in the given value for the area.
39
=
x
2
+
6
x
−
16
Next, we simplify by moving all terms to one side and factor the equation.
0
=
x
2
+
6
x
−
55
Finally, we factor the equation. This means we reverse-FOIL, trying to determine the two things that we multiplied together.
0=
(
x
−
5
)
⋅
(
x
+
11
)
If the equation ultimately equals zero, either (
x
−
5
) or (
x
+
11
) or both equal zero. Therefore, we set each equal to zero to find the value of
x
.
x
−
5
=
0
x
=
5
x
+
11
=
0
x
=
−
11
Since x is a length, we know it cannot be negative. Thus, we can conclude that it equals 5.
