the length of a rectangle is increased by 25%. by what percentage should the width be decreased so that the area of the rectangle remains unchanged
a 25% increase is a factor of 5/4
So, you need 4/5 of the width for the area to stay the same
(5/4 l)(4/5 w) = lw
So, what % decrease is 4/5?
To find out by what percentage the width should be decreased, we need to understand the relationship between the length, width, and area of a rectangle.
Let's say the original length of the rectangle is L and the original width is W. The original area of the rectangle would be A = L * W.
When the length is increased by 25%, the new length becomes 1.25L (original length + 25% of the original length). The area of the new rectangle would be (1.25L) * W.
We want the area of the new rectangle to remain the same as the original area, so we can set up the equation:
A = (1.25L) * W
Since the areas are equal, we can simplify the equation:
L * W = (1.25L) * W
Dividing both sides of the equation by W:
L = 1.25L
Now, if we subtract L from both sides of the equation:
0 = 0.25L
The equation tells us that 0.25L is equal to zero, which means L is zero or the length of the rectangle is zero. However, a rectangle cannot have a length of zero.
Therefore, we can conclude that it is not possible to decrease the width by any percentage so that the area of the rectangle remains unchanged when the length is increased by 25%.