The length of a certain rectangle is quadrupled and the width is tripled. What is the ratio of the area of the new enlarged rectangle to the original rectangle?
old area A = LW
new area = (4L)(3W) = 12LW = 12A
Well, the new enlarged rectangle sounds like it's been on quite the growth spurt! If the length has been quadrupled and the width tripled, then we can say the new length is 4 times the original length and the new width is 3 times the original width.
Now, the area of a rectangle is found by multiplying the length by the width. So, if we take the new length (4 times the original length) and multiply it by the new width (3 times the original width), we get:
(4 times the original length) * (3 times the original width)
And if we break it down further, we get:
(4 * original length) * (3 * original width)
Now, let's compare this to the original area, which is just the original length multiplied by the original width:
(original length) * (original width)
So, the ratio of the new enlarged rectangle's area to the original rectangle's area is:
[(4 * original length) * (3 * original width)] / [(original length) * (original width)]
Simplifying this further, we get:
(4 * 3 * original length * original width) / (original length * original width)
The original length and original width cancel out, leaving us with:
(4 * 3) / 1
And finally:
12
So, the ratio of the area of the new enlarged rectangle to the original rectangle is 12. That's quite the big change!
To find the ratio of the area of the new enlarged rectangle to the original rectangle, we first need to calculate the area of each rectangle.
Let's assume the original length of the rectangle is L and the original width is W. Therefore, the area of the original rectangle is A = L * W.
For the new enlarged rectangle, the length is quadrupled, so the new length is 4L. The width is tripled, so the new width is 3W. Therefore, the area of the new enlarged rectangle is A' = (4L) * (3W) = 12L * W.
The ratio of the area of the new enlarged rectangle to the original rectangle is A' / A.
Substituting the values we found, the ratio is (12L * W) / (L * W).
Simplifying the expression, we find that the ratio is 12.
Therefore, the ratio of the area of the new enlarged rectangle to the original rectangle is 12:1.
To find the ratio of the area of the new enlarged rectangle to the original rectangle, we need to find the area of both rectangles and then calculate the ratio.
Let's assume the original length of the rectangle is L and the original width is W.
The area of the original rectangle is given by:
Original Area = L * W
Now, let's consider the enlarged rectangle. According to the problem, the length is quadrupled, which means the new length is 4L, and the width is tripled, which means the new width is 3W.
The area of the new enlarged rectangle is given by:
Enlarged Area = (4L) * (3W) = 12LW
To find the ratio of the areas, we divide the area of the new enlarged rectangle by the area of the original rectangle:
Ratio = Enlarged Area / Original Area = 12LW / LW
Simplifying the expression, we find:
Ratio = 12
Therefore, the ratio of the area of the new enlarged rectangle to the original rectangle is 12:1.