The height of a triangle is 4 in. greater than twice its base. The area of the triangle is no more than 168 in.2. Which inequality can be used to find the possible lengths, x, of the base of the triangle? mc015-1.jpg mc015-2.jpg mc015-3.jpg mc015-4.jpg

Letx-------> the length of the base of triangley-------> the height of the trianglewe know thatthe 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]thereforethe answer isThe 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]