A square storage area measures 10 m on a side. By how much must each side be shortened to decrease this area to less than half the original area? (3 marks - show your work)
since a square of side 10/√2 has half the area, each side needs to be shortened by at least by 10 - 10/√2
Can you please show your work as to how you got this answer?
To find out by how much each side must be shortened to decrease the area of the square storage area to less than half its original area, we first need to calculate the original area.
The formula for the area of a square is:
Area = side^2
Given that each side of the square measures 10 m, we can calculate the original area as follows:
Original Area = 10^2
Original Area = 100 m^2
To decrease the area to less than half of the original area, we need to find half of the original area:
Half of the Original Area = 1/2 * Original Area
Half of the Original Area = 1/2 * 100 m^2
Half of the Original Area = 50 m^2
Now, we can subtract this half area from the original area to find the difference:
Difference = Original Area - Half of the Original Area
Difference = 100 m^2 - 50 m^2
Difference = 50 m^2
Since the square has equal sides, we can distribute the difference equally among all four sides. To find out by how much each side must be shortened, we divide the difference by 4:
Each side must be shortened by:
Shortening Length = Difference / 4
Shortening Length = 50 m^2 / 4
Shortening Length = 12.5 m
Therefore, each side of the square storage area must be shortened by 12.5 meters to decrease the area to less than half the original area.