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)

10 * 10 = 100 square meters

x^2 < 50

7^2 < 50

To find out how much each side must be shortened to decrease the square's area to less than half the original area, we need to first calculate the original area of the square and then find the amount by which each side needs to be reduced.

1. Calculate the original area of the square:
The formula for the area of a square is A = s^2, where A represents the area and s represents the length of one side.
In this case, the length of one side is given as 10 m.
Substituting the values into the formula, we have: A = 10^2 = 100 m^2.

2. Calculate half the original area:
Half of the original area is (1/2) * 100 = 50 m^2.

3. Find the amount by which each side needs to be shortened:
To find this, we need to find the length of the side of a square with an area of 50 m^2.
We can use the formula A = s^2 and solve for s.
Substituting the value for A from step 2, we have: 50 = s^2.
Taking the square root of both sides, we get: s = √50 = 7.07 m (approximated to two decimal places).

The original side length was 10 m, and to decrease the area to less than half the original area, we need to shorten each side by 10 - 7.07 = 2.93 m (approximated to two decimal places).

Therefore, each side must be shortened by approximately 2.93 meters to decrease the area to less than half the original area.