Official Solution:
Given:
AS = 10 cm
SN = 5 cm
TN = 8 cm
Find:
What could be the value of AT?
Since we have been given the lengths of the triangle and we do not have any information on the angles of the triangles, we will have to use the side property of the triangle to solve this question.
In triangle ASN –AS = 10 cm, SN = 5 cm
We know that sum of two sides > third side and we also know that difference of two sides < third side, thus, we can write –
10-5 < AN < 10+5
5 < AN < 15
Thus the value of AN can be {6,7,8,9,10,11,12,13,14}
Find the maximum value of AT. In triangle ATN, we can write –
AT < AN + TN
AT < 14 + 8
AT < 22
Thus, we can say that the maximum value of AT is 21 units.
Now, let us find the minimum value of AT
In triangle ATN, we can write –
TN ~ AN < AT
From the possible value of AN - {6,7,8,9,10,11,12,13,14}, if we take AN = 8, we will get AT > 8 – 8
AT > 0
Thus, the minimum value of AT will be 1 unit.
Therefore, the positive difference between the maximum and minimum value of AT could be = ( 21 – 1) = 20 units
The correct answer is Option C.
_________________