Let's work through this problem step by step to find the maximum force that can safely be applied to the tile.
### Step 1: Identify the Dimensions of the Tile
The tile is given as a square with each side measuring 1.6 meters. We can confirm this since only one dimension is specified, typically implying a square shape.
[tex]\[ \text{Length of the tile} = 1.6 \text{ meters} \][/tex]
[tex]\[ \text{Width of the tile} = 1.6 \text{ meters} \][/tex]
### Step 2: Calculate the Area of the Tile
To find the area of a square tile, we use the formula for the area of a rectangle, which in this case simplifies to the area of a square:
[tex]\[ \text{Area} = \text{length} \times \text{width} \][/tex]
Plugging in the given dimensions:
[tex]\[ \text{Area} = 1.6 \text{ meters} \times 1.6 \text{ meters} \][/tex]
[tex]\[ \text{Area} = 2.56 \text{ square meters} \][/tex]
### Step 3: Understand the Given Pressure
We are given the maximum pressure that the tile can sustain, which is 200 Newtons per square meter (N/m²).
### Step 4: Calculate the Maximum Force
The problem states the relationship:
[tex]\[ \text{Pressure} = \frac{\text{Force}}{\text{Area}} \][/tex]
Rearranging this to solve for force, we get:
[tex]\[ \text{Force} = \text{Pressure} \times \text{Area} \][/tex]
Substituting the values for maximum pressure and area:
[tex]\[ \text{Force} = 200 \text{ N/m}^2 \times 2.56 \text{ m}^2 \][/tex]
[tex]\[ \text{Force} = 512 \text{ Newtons} \][/tex]
Therefore, the maximum force that can safely be applied to the tile is [tex]\( \boxed{512 \text{ Newtons}} \)[/tex].
