gautamsubrahmanyam wrote:
Figure is attached.
In the figure above if x and y each are less than 90 and PS|| QR ,is the length of segment PQ less than the length of segment SR?
(1) x>y
(2) x+y > 90
Since PS||QR the shortest distance between the lines PS and QR is the perpendicular between the lines. Whichever segment PQ or SR is closer to becoming a perpendicular is the shorter of the two segments. For this to happen the angles x or y must get maximized towards 90 degrees for their length to become minimum.
Statement 1
x > y
this implies that x is closer to 90 degrees than y. Hence PQ is closer to being perpendicular and thus we can say that PQ is shorter than SR. Sufficient.
Statement 2
x + y > 90
Does not tell us the relation between x and y. Here x could be greater than y (x = 80, y= 70) and satisfy the inequality, or x could be lesser than y (x = 70, y = 80) and still satisfy the inequality. Hence we cannot say which angle is closer to 90 degrees so we cannot determine which line is closer to becoming perpendicular and thus shorter. Not sufficient.
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