GEOMETRY The formula for the perimeter of a rectangle is P = 2 + 2w, where is the length and w is the width. A rectangle has a perimeter of 24 inches. Find its dimensions if its length is 3 inches greater than its width.
To find the dimensions of the rectangle, we will use the given information about its perimeter and the relationship between its length and width.
Let's start by assigning variables to the length and width of the rectangle. Let's say L represents the length and W represents the width.
According to the problem, the formula for the perimeter of a rectangle is given as P = 2L + 2W. We are also told that the perimeter of this particular rectangle is 24 inches. So we can write the equation as:
24 = 2L + 2W
Since the length is given as "3 inches greater than its width," we can write the relationship as L = W + 3.
Now, substitute the value of L in terms of W into the equation for the perimeter:
24 = 2(W + 3) + 2W
Distribute the 2 to both terms inside the parentheses:
24 = 2W + 6 + 2W
Combine like terms:
24 = 4W + 6
Subtract 6 from both sides of the equation:
24 - 6 = 4W
18 = 4W
Divide both sides of the equation by 4:
18/4 = W
W = 4.5
Now that we have the value of W, we can substitute it back into the equation for L:
L = W + 3
L = 4.5 + 3
L = 7.5
Therefore, the width of the rectangle is 4.5 inches and the length is 7.5 inches.
2w + 2(w+3) = 24
Now find w, and thus w+3