If the length of a rectangle is increased by 10% and the width is decreased by 10%, is the are changed? If so, does it increase or decrease and by what percent? Please explain, I’m so confused
.9 * 1.1 = 0.99 which is less than 1
To determine whether the area of a rectangle changes when the length is increased by 10% and the width is decreased by 10%, we need to understand the formula for the area of a rectangle, which is length multiplied by width.
Let's assume the original length of the rectangle is L and the original width is W.
The area of the rectangle is given by: A = L x W
After increasing the length by 10%, it becomes 1.1L (10% of L is L * 0.1 = 0.1L).
After decreasing the width by 10%, it becomes 0.9W (10% of W is W * 0.1 = 0.1W).
Now, the new area of the rectangle can be calculated using the new length and width:
New Area (A') = (1.1L) x (0.9W) = 0.99LW, which is 0.99 times the original area.
So, the new area is 0.99 times (99% of) the original area.
Therefore, the area decreases by 1% when the length is increased by 10% and the width is decreased by 10%.
To summarize:
- When the length is increased by 10% and the width is decreased by 10%, the area of the rectangle decreases by 1%.
- The area of the rectangle changes from A to 0.99A, which means the new area is 99% of the original area.