Question

The trapezoid below has legs with lengths y feet and one base that is four feet longer than the other base, x.A.) The perimeter of this trapezoid is given by P=2x + 2y + 4. Solve this equation for the leg length, y.B.) If the perimeter of the figure is 26 feet and the shorter base, x, is 8 feet, then find the length of the leg, y.SORRY ABOUT MY FACE BEING IN THE PICTURE

Answer 1

A.

Solving the equation for the leg y will give;

`y=(P-2x-4)/(2)`

B.

The length of the leg y is;

`y=3ft`

Step-by-step explanation:

Given that the perimeter of this trapezoid is given by;

`P=2x+2y+4`

A.

Solving for y, we have;

`\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=(P-2x-4)/(2) \end{gathered}`

solving the equation for the leg y will give;

`y=(P-2x-4)/(2)`

B.

If the perimeter of the figure is 26 feet and the shorter base, x, is 8 feet;

`\begin{gathered} P=26ft \\ x=8ft \end{gathered}`

Substituting;

`\begin{gathered} y=(P-2x-4)/(2) \\ y=(26-2(8)-4)/(2)=(26-16-4)/(2) \\ y=(26-20)/(2)=(6)/(2) \\ y=3ft \end{gathered}`

Therefore, the length of the leg y is;

`y=3ft`