the perimeter of a rectangle is 32 m. The length is 4m more than twice the width
P = 2L + 2W
32 = 2(2W + 4) + 2W
32 = 4W + 8 + 2W
24 = 6W
4 = W
To find the dimensions of the rectangle, we can set up an equation based on the given information.
Let's assume the width of the rectangle is "w" meters. According to the given information, the length is "4m more than twice the width." Therefore, the length can be expressed as (2w + 4) meters.
The formula for the perimeter of a rectangle is P = 2l + 2w, where P represents the perimeter, l represents the length, and w represents the width.
Plugging in the given values, we have:
32 = 2(2w + 4) + 2w
To solve for w, we first simplify the equation:
32 = 4w + 8 + 2w
32 - 8 = 6w
24 = 6w
Next, we isolate the variable w:
w = 24 / 6
w = 4
Now that we have the width, we can substitute it back into either the length equation or the perimeter formula to find the length.
Using the length equation (l = 2w + 4):
l = 2(4) + 4
l = 8 + 4
l = 12
Therefore, the width of the rectangle is 4 meters and the length is 12 meters.