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07 Jan 2021, 01:15
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ABCD is a rectangle. If side AB is 8 units long and side BC is 6 units long, which are possible lengths of line DX?
I. 5
II. 6
III. 7
A. I only
B. III only
C. I and II only
D. I and III only
E. I, II and III
Attachment:
1.png [ 48.05 KiB | Viewed 3871 times ]
07 Jan 2021, 02:03
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No side of any triangle can be equal to or longer than its hypotenuse. If the hypotenuse of triangle DXA is 6 and CYB is 6, then it can be only 5.
Hence Option 1
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Hence Option 1
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07 Jan 2021, 04:05
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Bunuel
ABCD is a rectangle. If side AB is 8 units long and side BC is 6 units long, which are possible lengths of line DX?
I. 5
II. 6
III. 7
A. I only
B. III only
C. I and II only
D. I and III only
E. I, II and III
Attachment:
1.png
Since AB is 8 and BC is 6, the diagonal AC's length is 10 (pythagorean triplet 3-4-5). So length of DB will be 10 too.
X and Y are any points on AC such that X is to the left of Y.
X and Y will overlap to give us the diagonal DB. In that case, both DX and BY will be 5 each.
Keep moving X to the left and DX will keep going smaller till it becomes the altitude which will be its smallest length and then it will start increasing again, it will reach 5 again at some point and then it will reach just less than 6 (the length of DA).
So out of 5, 6 and 7, the only value that DX can take is 5.
Answer (A)
