Question

CorrectQuestion 4 of 11. Step 1 of 1The perimeter of a rectangle is 110 meters and the length is 5 meters longer than the width. Find the dimensions of the rectangle. Let x = the length and y = the width 2x+ 2y = 110X-y=5Solve the system graphically.

Answer 1

Recall that to graph a line we need two points on the line.

Substituting x=0 in the first equation we get:

`\begin{gathered} 2*0+2y=110, \\ 2y=110, \\ y=55. \end{gathered}`

Therefore the graph of the first equation passes through (0,55).

Substituting y=0 in the first equation we get:

`\begin{gathered} 2x+2*0=110, \\ 2x=110, \\ x=55. \end{gathered}`

Therefore the graph of the first equation passes through (55,0).

Then, the graph of the first equation is:

Now, substituting x=0 in the second equation we get:

`\begin{gathered} 0-y=5, \\ -y=5, \\ y=-5. \end{gathered}`

Therefore the second equation passes through (0,-5).

Substituting y=0 in the second equation we get:

`\begin{gathered} x-0=5, \\ x=5. \end{gathered}`

Therefore the second equation passes through (5,0).

Then, the graph of the second equation is:

Now, notice that the intersection of both graphs is:

Answer: x=30 and y=25.