If length of one side of a 3x3 square is four times, and the length of the adjacent side is tripled, the perimeter of the new rectangle is how many times bigger than the perimeter of the original square?
please explain and show work.
One side is now 4*3 = 12 and the other side is 3*3 = 9 so the new perimeter must be 12+12+9+9 = ?
The original perimeter is 3+3+3+3 = ?
Now compare.
To solve this problem, let's start by finding the perimeter of the original 3x3 square.
The formula to calculate the perimeter of a square is P = 4s, where P is the perimeter and s is the length of one side.
In this case, the length of one side of the original square is 3 units. Plugging this value into the formula, we get:
P = 4 * 3
P = 12
So, the perimeter of the original 3x3 square is 12 units.
Now, let's calculate the perimeter of the new rectangle that is formed by increasing one side by four times and the adjacent side by three times.
Let's assume the length of the increased side is 3n (since it is four times the original side), and the length of the adjacent side is 3m (since it is three times the original side).
The formula to calculate the perimeter of a rectangle is P = 2(l+w), where P is the perimeter, l is the length, and w is the width.
In this case, the length of the rectangle is 3n, and the width is 3m. Plugging these values into the formula, we get:
P = 2(3n + 3m)
Simplifying further:
P = 6n + 6m
To find how many times bigger the perimeter of the new rectangle is compared to the original square, we need to calculate the ratio of the new perimeter to the original perimeter.
Ratio = (Perimeter of the New Rectangle) / (Perimeter of the Original Square)
Ratio = (6n + 6m) / 12
Ratio = (6/12) * (n + m)
Ratio = (1/2) * (n + m)
Therefore, the perimeter of the new rectangle is (1/2) times bigger than the perimeter of the original square.
To find an exact numerical value, we would need the values of n and m.