6. Raju invited his friend George for a dinner at his house When George asked for the direction of
Raju's house Raju gave him the following instruction
Proceed 140 metres south from your house then walk 200 metres to east. Then turn to north and
walk 100 metres. After that walk 160 metres to west
What is the shortest distance between the two houses and the direction to Raju's house from
Georges house?
-10v 2 metres and north-west
0 metres and south east
BO metres and south-east.
80 metres and north-west
Answers
The shortest distance is x = 40√2 from south to east.
We are given that:
- Distance covered towards south = 140m
- Distance covered towards east = 200m
- Distance covered towards north = 100m
- Distance covered towards west = 160m
To Find: The shortest distance between the two houses
Solution:
- We have a triangle while traveling from George to Raju's house.
- x = √40^2 + 40^2
- x = √3200
- x = √1600 x 2
- x = 40√2
- Thus the shortest distance is x = 40√2 from south to east.
#SPJ3
Answer:
Step-by-step explanation: As George is walking 140m south, mark that point as F.
Next he walks 200m east, mark that point E.
Next he turns North and walks 100m, mark that point D.
Next he walks 160m to the west, mark that point B.
Now the shortest distance he walked from his house to Raju's house is the hypotenuse of the triangle ABC where C is the origin (his house), B is Raju's house and A is a path drawn from Raju's house.
AB = AD-BD
⇒ 200-160
AB = 40m
AC = CF-AF
⇒ 140-100
AC = 40m
So, by hypotenuse theorum,
A² + B² = C²
⇒ (AB)² + (AC)² = (BC)²
⇒ (40)² + (40)² = (BC)²
⇒ (1600) + (1600) = (BC)²
⇒ 3200 = (BC)²
⇒ √3200 = BC
⇒40√2 = BC
∴The shortest distance between the two houses is 40√2m and the direction to Raju's house from George's house is South-East