Let
x-------> the length of the base of triangle
y-------> the height of the triangle
we know that
the area of the triangle is equal to
[tex]A=\frac{1}{2}xy[/tex]
in this problem we have
[tex]A \leq 168\ in^{2}[/tex]
so
[tex]\frac{1}{2}xy\leq 168[/tex] --------> equation [tex]1[/tex]
[tex]y=2x+4[/tex] --------> equation [tex]2[/tex]
Substitute equation [tex]2[/tex] in equation [tex]1[/tex]
[tex]\frac{1}{2}x[2x+4]\leq 168[/tex]
[tex]x^{2}+2x \leq 168[/tex]
therefore
the answer is
The inequality that can be used to find the possible lengths, x, of the base of the triangle is [tex]\frac{1}{2}x[2x+4]\leq 168[/tex] or [tex]x^{2}+2x \leq 168[/tex]
