the perimeter of a rectangle is 24 inches. find the dimensions if the length is 3 inches greater than its width
Let x = width.
2x + 2(x + 3) = 24
4x + 6 = 24
4x = 18
x = ?
To find the dimensions of a rectangle given its perimeter and the relationship between its length and width, we can set up an equation and solve for the unknowns.
Let's assume that the width of the rectangle is "x" inches. Since the length is 3 inches greater than the width, the length can be expressed as "x + 3" inches.
The perimeter of a rectangle is calculated by adding the lengths of all its sides, which, in this case, is the sum of the lengths of the two widths and two lengths:
Perimeter = 2(width) + 2(length)
Substituting the values we have into the equation, we get:
24 = 2(x) + 2(x + 3)
Next, we simplify and solve for "x":
24 = 2x + 2x + 6
24 = 4x + 6
24 - 6 = 4x
18 = 4x
x = 18/4
x = 4.5
Therefore, the width, "x", is 4.5 inches, and the length, "x + 3", is 7.5 inches.
So, the dimensions of the rectangle are 4.5 inches (width) by 7.5 inches (length).