Answer :
To find the width of the rectangle with a given perimeter of 60 inches and the length being 2 less than 3 times the width, set up equations based on these relationships and solve for the width, resulting in a width of 8 inches that is option A is correct.
The student is asking how to find the width of a rectangle given that the length is 2 inches less than 3 times its width and the perimeter is 60 inches. To solve this, we can set up two equations based on the information given:
The length L of the rectangle is L = 3W - 2, where W is the width.
The perimeter P is P = 2L + 2W, and we know that P = 60 inches.
Substitute the expression for L into the perimeter equation to get:
60 = 2(3W - 2) + 2W
Which simplifies to:
60 = 6W - 4 + 2W
Combine like terms to get:
60 = 8W - 4
Add 4 to both sides to get:
64 = 8W
Finally, divide both sides by 8 to find W:
W = 64 / 8
W = 8 inches.
Therefore, the width of the rectangle is 8 inches, which matches answer choice A.
