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06 Nov 2022, 02:32
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In the figure above, line segments JK and LM represent two positions of the same board leaning against the side of KN of a wall. The length of KN is how much greater than the length of MN?
(1) The length of LN is \(\sqrt{2}\) meters.
(2) The length of JN is 1 meter.
Attachment:
2022-11-06_13-30-46.png [ 171.02 KiB | Viewed 1456 times ]
Attachment:
Kaplan.jpg [ 143.84 KiB | Viewed 1217 times ]
06 Nov 2022, 08:30
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In the figure above, line segments JK and LM represent two positions of the same board leaning against the side of KN of a wall. The length of KN is how much greater than the length of MN?
(1) The length of LN is \(\sqrt{2}\) meters.
(2) The length of JN is 1 meter.
Attachment:
2022-11-06_13-30-46.png
Attachment:
Kaplan.jpg
The key to this question is the term 'same board', hence ML = KJ
We need to find KN - MN
We know that \(\angle MNJ\) = \(\angle KNL\) = 90
Also the one of the angle of each triangle is given , so we can find the other angle.
If we know the length of one side of each triangle, we can find the length of all of the sides.
Statement 1
(1) The length of LN is \(\sqrt{2}\) meters.
The length of LN is given, LN is the side corresponding to \(\angle LMN = 45^{\circ}\)
Hence in \( \triangle LMN \)
- We can find the length of LM (side corresponding to \(\angle MNL = 90^{\circ}\)), and once we know LM , we have also found out KJ.
- We can find the length of MN, side corresponding to \(\angle MLN = 45^{\circ}\)
In\( \triangle KJN\), because we know the length of one side and we have the information of all the angles in the triangle, we can find the length of all other sides.
Hence this statement is sufficient and we can rule out B, C and E.
Statement 2
Similar to statement 1, we have the length of one side of \( \triangle KJN\), hence we can find the length of all the sides. And as we know KJ = ML, we know one side and all angles of \( \triangle MLN\). Hence this statement is sufficient as well.
Option D
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