Answer:
It is faster to walk through the field and directly to Ah Chong's house.
The difference between the distance via the road and through the field is 26 m.
Step-by-step explanation:
The scenario can be modeled as a right triangle (see attached diagram).
Option 1
- Walk 195 m west and 28 m north.
⇒ Total distance = 195 + 28 = 223 m
Option 2
- Walk directly to Ah Chong's house through the field.
To calculate this distance (hypotenuse of the right triangle), use Pythagoras Theorem.
Pythagoras Theorem
[tex]a^2+b^2=c^2[/tex]
where:
- a and b are the legs of the right triangle.
- c is the hypotenuse (longest side) of the right triangle.
[tex]\implies 195^2+28^2=c^2[/tex]
[tex]\implies c^2=38025+784[/tex]
[tex]\implies c^2=38809[/tex]
[tex]\implies c=\sqrt{38809}[/tex]
[tex]\implies c=197[/tex]
Therefore, the distance for option 2 is 197 m.
Difference
Option 1 - Option 2 = 223 - 197 = 26 m
Conclusion
As 197 < 223, it is faster for Rahmat to walk through the field and directly to Ah Chong's house (option 2).
Learn more about Pythagoras Theorem here:
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