The length of a rectangle is 4 times its width. If the length of the rectangle is cut in half, the new perimeter is which percent of the original perimeter
write an expression in simple form to represent the perimeter of a rectangle whose length is represented by 3x+1 and width is represented by 5x-6
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To determine the new perimeter after the length of the rectangle is cut in half, we first need to find the original perimeter and then calculate the new perimeter.
Let's assume the width of the rectangle is "w" units. Since the length of the rectangle is 4 times its width, the length would be "4w" units.
The formula for the perimeter of a rectangle is: P = 2(length + width)
For the original rectangle:
Length = 4w
Width = w
Using the formula, the original perimeter (P1) would be: P1 = 2(4w + w) = 10w
Now, when the length of the rectangle is cut in half, the new length becomes half of its original length, which would be 4w/2 = 2w.
For the new rectangle:
Length = 2w (half of the original length)
Width = w (same as the original width)
Using the formula again, the new perimeter (P2) would be: P2 = 2(2w + w) = 6w
To find the percentage of the new perimeter compared to the original perimeter, we can use the following formula:
Percentage = (P2 / P1) * 100
Substituting the values, we get: Percentage = (6w / 10w) * 100
Simplifying further, the "w" unit cancels out, leaving us with: Percentage = 6/10 * 100 = 60%
Therefore, the new perimeter is 60% of the original perimeter after the length of the rectangle is cut in half.