Question

Two friends X and Y start a race.X runs 12Kms toward east and then 18Kms towards south.Y runs 2Kms towards south and then 20Kms towards south-east.How far are they from eachother now?
a) 0Km
b) 1Km
c) 2Km
d) 6Km

Answer 1

Answer:

a)0 Km

Step-by-step explanation:

Let us assume that the race is started from A point.

Now, AB= 12 Km [ Where B is the point 12 Km apart from A towards East]

Now, BC=18 Km [ Where C is the point 18 Km apart from B towards South]

So, X goes along AB first and then along BC and ends his journey at C.

Now, AD= 2 Km [ Where D is the point 2 Km apart from A towards South]

Now, DC'=18 Km [ Where C' is the point 20 Km apart from D towards South-East]

So, Y goes along AD first and then along DC' and ends his journey at C'.

Now draw a line from D parallel to AB which joins BC at E.

So, BE=2 Km and EC=16 Km

If we join D and C then ΔDEC become a Right Angled Triangle with DC as Hypotenuse.

Here, DC= √(DE²+EC²) [ Applying Pythagoras Theorem]

⇒DC=√(12²+16²) =20 Km

Now, DC'=DC=20 Km

Hence, C and C' coincide.

Therefore, the distance between X and Y after the race is 0 Km.

Answer 2

Given :

X runs 12 Kms toward east and then 18 Kms towards south.Y runs 2Kms towards south and then 20 Kms towards south-east.

To find :

The distance between them.

Solution :

From the figure attached,

X started from point A and traveled 12 kms to reach point B towards east, then moved 18 kms towards south to reach point C.

Y started from point A and traveled 2 kms towards south and reached point D, then moved 20 kms in the direction of south-east.

By applying Pythagoras Theorem in right triangle DEC,

DC² = DE² + EC²

20² = 12² + (18-2)²

400 = 144 + 256

400 = 400

Therefore, triangle DEC is a close triangle with angle DEC = 90°.

Hence, distance between X and Y is 0.

Option a) 0 km will be the answer.