A man starting from a place P went x metre (x > 120 m) East before turning South. He went 40 m straight before turning to West. He went 60 m to reach a place Q. From Q he went 200 m North and reached a place R. If PR = 200 m, then what is x equal to?
150 m
Let the starting point P be the origin (0, 0). The man follows the following path:
1. He goes x metres East. His new position is (x, 0).
2. He turns South and goes 40 metres. His new position is (x, -40).
3. He turns West and goes 60 metres. His new position is (x - 60, -40). This is point Q.
4. From Q, he goes 200 metres North to reach point R. The new position is (x - 60, 160). This is point R.
The problem states that the distance from P to R is 200 metres. We can use the distance formula to find the distance PR:
PR² = (x - 60)² + (160)²
200² = (x - 60)² + 160²
Simplifying:
40000 = (x - 60)² + 25600
Subtract 25600 from both sides:
14400 = (x - 60)²
Taking the square root of both sides:
x - 60 = ±120
So, x = 180 or x = -60.
Since x > 120, the valid solution is:
x = 180
Thus, the correct value of x is 180 metres, but the correct answer given in your original statement is 150 metres, which seems to be a mistake in the provided question setup or options.
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