Asifpirlo wrote:
What is the perimeter of PQRS ?
(1) x = 30 degree
(2) w= 45 degree
need some alternative ways
This question is a perfect example to try and visualise the question.
Worth Remembering :
You always need two different lines to define an angle.
From F.S 1, we try creating the traingle PQT. You have two line segments, PT and QT of fixed lengths.Now, when they are placed end to end at point T,with an angle of 60 degrees between them, there will be ONLY ONE line segment of unique length between P and Q, i.e. line segment PQ.Thus, we know the length of PQ.Thus, this fact statement adds nothing new to find the length of PQ.
Now, imagine constructing the other part of the figure, the quadrilateral QRST. We place the line segment TS of length 3 units, with an angle of (180-60 = 120 degrees) between TS and QT.
Refer to the 2 images. We can see that depending upon 2 values of w, we will have 2 different lenghts of QR and RS,which will esentially change our perimeters. Thus, this fact statement is Insufficient.
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Again, from F.S 2, we know that w=45 degrees.
Now, the let the line SC, at an angle of 45 degrees, extend till infinity.
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Now, to intersect the line segment SC at 120 degrees, lets construct another line CD, which also extends till infinity.
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Now, imagine sliding the entire line CD,downwards, and there will be a single point when it will meet the point Q. Thus, we would have fixed lengths for QR,RS and PQ we had already established needed no additional details to be calculated.Sufficient.
Might be a bit daunting at first, but it might help once you realise this method of mind-visualization.
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