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09 Aug 2017, 04:45
Kudos
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
65%
(hard)
Question Stats:
50% (01:50) correct
50%
(02:00)
wrong
based on 88
sessions
History
Date
Time
Result
Not Attempted Yet
One side of a triangle has length 6 and a second side has length 7. Which of the following could be the area of this triangle?
I. 13
II. 21
III. 24
(A) I only
(B) II only
(C) III only
(D) I and II only
(E) I, II and III
I. 13
II. 21
III. 24
(A) I only
(B) II only
(C) III only
(D) I and II only
(E) I, II and III
09 Aug 2017, 05:31
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Bunuel
Hi...
Two points...
1. Area of triangle can be just slightly above 0 at the lower end.
2. The largest area will be right angle triangle with these sides
Ok lower end...Just above 0
Upper end... \(\frac{1}{2}*6*7=21\)
So 13 and 21 is possible, but 24 is NOT possible
D
09 Aug 2017, 15:26
Kudos
Bookmarks
Nice one.
Here is what I did on this one -->
Side 1 -> 6
Side 2 -> 7
Maximum area would be when the two sides are perpendicular to each other forming a right triangle.
Hence Max. Area -> 1/2 * 6 * 7 => 21
Minimum area => When the third side would of length zero and the triangle would cease to exist.
Hence the range of Areas => [0,21]
Hence Option 1 and Option 2 are possible.
Option 3 is not.
Hence D.
Here is what I did on this one -->
Side 1 -> 6
Side 2 -> 7
Maximum area would be when the two sides are perpendicular to each other forming a right triangle.
Hence Max. Area -> 1/2 * 6 * 7 => 21
Minimum area => When the third side would of length zero and the triangle would cease to exist.
Hence the range of Areas => [0,21]
Hence Option 1 and Option 2 are possible.
Option 3 is not.
Hence D.
