To find the dimensions of the rectangle, we start by defining the width of the rectangle as w. According to the problem, the length is 3 cm greater than the width, so we can express the length as l = w + 3.
The formula for the perimeter P of a rectangle is given by:
P = 2(l + w)
We know the perimeter is 24 cm, so we can set up the equation:
24 = 2((w + 3) + w)
Simplifying the equation:
24 = 2(2w + 3)
24 = 4w + 6
Next, we subtract 6 from both sides:
24 – 6 = 4w
18 = 4w
Now, divide both sides by 4:
w = 4.5
Now that we have the width, we can find the length:
l = w + 3 = 4.5 + 3 = 7.5
Therefore, the dimensions of the rectangle are:
Width: 4.5 cm
Length: 7.5 cm