Answer:
A.
Solving the equation for the leg y will give;
[tex]y=\frac{P-2x-4}{2}[/tex]
B.
The length of the leg y is;
[tex]y=3ft[/tex]
Explanation:
Given that the perimeter of this trapezoid is given by;
[tex]P=2x+2y+4[/tex]
A.
Solving for y, we have;
[tex]\begin{gathered} P=2x+2y+4 \\ \text{subtract 2x+4 from both sides;} \\ P-(2x+4)=2x+2y+4-(2x+4) \\ P-2x-4=2x+2y+4-2x-4 \\ P-2x-4=2x-2x+2y+4-4 \\ P-2x-4=2y \\ 2y=P-2x-4 \\ y=\frac{P-2x-4}{2} \end{gathered}[/tex]
solving the equation for the leg y will give;
[tex]y=\frac{P-2x-4}{2}[/tex]
B.
If the perimeter of the figure is 26 feet and the shorter base, x, is 8 feet;
[tex]\begin{gathered} P=26ft \\ x=8ft \end{gathered}[/tex]
Substituting;
[tex]\begin{gathered} y=\frac{P-2x-4}{2} \\ y=\frac{26-2(8)-4}{2}=\frac{26-16-4}{2} \\ y=\frac{26-20}{2}=\frac{6}{2} \\ y=3ft \end{gathered}[/tex]
Therefore, the length of the leg y is;
[tex]y=3ft[/tex]
