To solve the problem of finding the area of the base of the box given the pressure and the force it exerts, we can use the relationship between pressure, force, and area, which is given by the formula:
[tex]\[ \text{Pressure} = \frac{\text{Force}}{\text{Area}} \][/tex]
Given:
- The pressure ([tex]\( P \)[/tex]) is [tex]\( 200 \, \text{N/m}^2 \)[/tex]
- The force ([tex]\( F \)[/tex]) is [tex]\( 140 \, \text{N} \)[/tex]
We need to find the area ([tex]\( A \)[/tex]) of the base of the box. Rearranging the formula to solve for the area, we have:
[tex]\[ \text{Area} = \frac{\text{Force}}{\text{Pressure}} \][/tex]
Substitute the given values into the formula:
[tex]\[ \text{Area} = \frac{140 \, \text{N}}{200 \, \text{N/m}^2} \][/tex]
Now, perform the division:
[tex]\[ \text{Area} = 0.7 \, \text{m}^2 \][/tex]
So, the area of the base of the box is [tex]\( 0.7 \, \text{m}^2 \)[/tex].
Since the problem asks for the answer to be given to one decimal place, we confirm that the area [tex]\( 0.7 \, \text{m}^2 \)[/tex] is already in the required format.
Thus, the area of the base of the box is [tex]\( 0.7 \, \text{m}^2 \)[/tex].
