Question

The perimeter of a rectangle is 56 inches. The length is 4 more than 3 times the width. What are the dimensions of the rectangle?

Write the system of equations that would be used to solve this problem

Answer 1

Perimeter of a rectangle: 2l+2w=56
Since the length is 4 more than 3 times the width, then l=3w+4
Thus,
\[P=2(3w+4)+2w=56\]
\[6w+8+2w=56\]
\[8w+8=56\]
Then:\[8w=48\]
\[w=6\]
Then plug it back into the length equation to find length:
\[l=3(6)+4\]
\[l=22\]

Now width is 6 inches. If the length is 4 more than 3 times then width, then it should be 22, which is what I got.

Answer 2

L=3w+4
P=2(w+L)=2(w+3w+4)=56
8w+8=56