A 2009 by 2009 square has its length decreased by 50 and its width increased by 50. By how much does its area change?
Thank you for your help!
2009 * 2009 = 4,036,081 square units
2,059 * 1,959 = ?
2059 × 1959 =
4033581
2009 x 2009 = 4036081
4036081 - 4033581 = 2500
To find the change in area, we need to calculate the area of the original square and the area of the new rectangle and then find the difference between the two.
Let's start with the original square:
The length and width of the original square are both equal to 2009.
So, the area of the original square = length * width = 2009 * 2009 = 4,036,081.
Now, let's calculate the area of the new rectangle:
The length of the new rectangle = original length - 50 = 2009 - 50 = 1959.
The width of the new rectangle = original width + 50 = 2009 + 50 = 2059.
So, the area of the new rectangle = length * width = 1959 * 2059 = 4,025,781.
To find the change in area, we subtract the area of the original square from the area of the new rectangle:
Change in area = Area of new rectangle - Area of original square
= 4,025,781 - 4,036,081
= -10,300.
Therefore, the area of the square changes by -10,300.
To find the change in area of the square, we need to first compute the area of the original square and the area of the modified square, and then subtract the original area from the modified area.
The area of a square is calculated by multiplying the length of one side by itself. In this case, the original square has sides of length 2009 units, so its area is 2009 * 2009 = 4,036,081 square units.
To find the dimensions of the modified square, we decrease the length by 50 units and increase the width by 50 units. The length of the modified square is 2009 - 50 = 1959 units, and the width is 2009 + 50 = 2059 units.
To find the area of the modified square, we multiply the modified length by the modified width: 1959 * 2059 = 4,036,781 square units.
Finally, we subtract the original area from the modified area to find the change in area: 4,036,781 - 4,036,081 = 700 square units.
Therefore, the area of the square changes by 700 square units when the length is decreased by 50 and the width is increased by 50.