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A rectangular floor tile is shown with dimensions given to the nearest 0.1 meter.

Dimensions: 1.6 m

The tile can sustain a maximum pressure of 200 Newtons per square meter (N/m²), correct to the nearest 5 N/m².

Given that Pressure = Force / Area, work out the maximum force, in Newtons, that can safely be applied to the tile.

(Optional working)
Force =

Answer: _________


Sagot :

To determine the maximum force that can safely be applied to the tile, follow these detailed steps:

1. Identify the dimensions of the tile:
- The length of the tile is given as 1.6 meters.
- The width of the tile is assumed to be the same since no other width is given, making it a square tile with a width of 1.6 meters.

2. Calculate the area of the tile:
- Area of a rectangle (or square in this case) is calculated by multiplying the length by the width.
[tex]\[ \text{Area} = \text{length} \times \text{width} \][/tex]
Substituting the given dimensions:
[tex]\[ \text{Area} = 1.6\ \text{meters} \times 1.6\ \text{meters} = 2.56\ \text{square meters} \][/tex]

3. Determine the maximum pressure the tile can sustain:
- The given maximum pressure is 200 Newtons per square meter.

4. Calculate the maximum force:
- Using the formula that relates pressure, force, and area:
[tex]\[ \text{Pressure} = \frac{\text{Force}}{\text{Area}} \][/tex]
Rearrange the formula to solve for Force:
[tex]\[ \text{Force} = \text{Pressure} \times \text{Area} \][/tex]
Substitute the maximum pressure and the area of the tile:
[tex]\[ \text{Force} = 200\ \text{N/m}^2 \times 2.56\ \text{m}^2 = 512\ \text{Newtons} \][/tex]

Therefore, the maximum force that can safely be applied to the tile is:

[tex]\[ \boxed{512\ \text{Newtons}} \][/tex]
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