Question

Seven towns T1, T2, T3, T4, T5, T6 and T7 are
situated as follows
T5 is 8 km to the west of T2
To is 8 km to the north of T1
T4 is 8 km to the south of T7
T7 is 8 km to the east of T3
T3 is 4 km to the west of T1
T4 is exactly in the middle of T2 and T5
How far is T1 from Tz​

Answer 1

Given :- Seven towns T1, T2, T3, T4, T5, T6 and T7 are

situated as follows :-

• T5 is 8 km to the west of T2
• T6 is 8 km to the north of T1
• T4 is 8 km to the south of T7
• T7 is 8 km to the east of T3
• T3 is 4 km to the west of T1
• T4 is exactly in the middle of T2 and T5.

To Find :-

• How far is T1 from T4 ?

Solution :-

from image Position of all are shown .

As given that,

• T7 is 8 km to the east of T3
• T3 is 4 km to the west of T1 .

we get,

→ T1 is = (8 - 4) = 4km to the west of T7.

and,

• T4 is exactly in the middle of T2 and T5.
• T4 is 8 km to the south of T7. .

So,

→ T4 to T7 = 8 km .

Now, from second diagram of image we get,

→ T4 to T7 = 8km.

→ T7 to T1 = 4km .

Therefore,

→ T1 to T4 = √[(T4 to T7)² + (T7 to T1)²] { By pythagoras Theorem. }

→ T1 to T4 = √[(8)² + (4)²]

→ T1 to T4 = √[64 + 16]

→ T1 to T4 = √(80)

→ T1 to T4 = 4√5 km . (Ans.)

Hence, T1 is 4√5km far from T4 .

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