a rectangle rug has a perimeter of 146 ft the width of the rug is 5 feet more than three times the length find the length and the width

The length = 56 feet and the width = 17 feet.

Step-by-step explanation:

We can set up 2 equations to solve this. Let the length of the rug be x, then

x = 3w + 5 where w = the width. (looks like you got the width and the length mixed up. The length is the longest side)

The perimeter = 2x + 2w = 146 so we have the 2 equations:

x = 3w + 5

2x + 2w = 146

Now we substitute for x in the second equation:

2 (3w + 5) + 2w = 146

6w + 10 + 2w = 146

8w = 136

w = 17 feet,

and x = 3 (17) + 5 = 56 feet.

Length is 17 feet and Width is 56 feet.

Step-by-step explanation:

P=2L+2W

146=2L+2 (3L+5)

146=2L+6L+10

146=8L+10L

146-10=8L+10-10

136=8L

136/8=8/8

17=L

W=3L+5

=3 (17) + 5

=56