Final answer:
The width of the rectangle is 3 inches, and the length is 9 inches, as the length is 3 times the width and the perimeter is 24 inches.
Step-by-step explanation:
To find the length and width of the rectangle with a perimeter of 24 inches where the length is 3 times the width, we need to set up equations based on the information provided.
Let W represent the width. Then the length, being 3 times the width, is 3W.
The perimeter (P) of a rectangle is given by the formula P = 2l + 2w, where l is the length and w is the width.
Substituting the given perimeter and expressions for length and width, we have 24 = 2(3W) + 2W. Simplifying, we get 24 = 6W + 2W, which becomes 24 = 8W.
Dividing both sides by 8 gives us W = 3.
Thus, the width is 3 inches.
The length is 3 times the width, so it is 3 * 3 = 9 inches.
The rectangle has dimensions of length 9 inches and width 3 inches.