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29 Nov 2014, 20:11
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
53% (01:25) correct
47%
(01:47)
wrong
based on 525
sessions
History
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If two sides of a triangle are 6 and 12, respectively, which of the following could NOT be the area of this triangle?
A. 1
B. 6
C. 17
D. 29
E. 38
Bunuel could you help!
A. 1
B. 6
C. 17
D. 29
E. 38
Bunuel could you help!
Official answer from veritas:
Solution: E.
If you know two sides of a triangle, the maximum area of the triangle can be obtained by setting these two sides as the base and height of a right triangle. For our triangle this gives us a maximum area of (6 * 12) / 2, or 36, so anything higher than this is invalid and the answer is (E). An alternative approach is to consider the minimum possible value of the triangle. Say we violated our third side rule and set the triangle's sides as 6, 12, and 18, respectively. Our "maximum" area here would be the set the base as 18, but since the triangle has no height -- the three sides only "fit together" as two parallel lines -- the height is 0 and the area is 0. But were we to extend one of the other two sides by an infinitesimally small amount, our area would be infinitesimally greater than 0, so presumably our minimum value is merely above zero. This means the greatest answer choice will be the number that violates the rule, and since no answer violates our minimum, (E) must again be the correct choice.
Solution: E.
If you know two sides of a triangle, the maximum area of the triangle can be obtained by setting these two sides as the base and height of a right triangle. For our triangle this gives us a maximum area of (6 * 12) / 2, or 36, so anything higher than this is invalid and the answer is (E). An alternative approach is to consider the minimum possible value of the triangle. Say we violated our third side rule and set the triangle's sides as 6, 12, and 18, respectively. Our "maximum" area here would be the set the base as 18, but since the triangle has no height -- the three sides only "fit together" as two parallel lines -- the height is 0 and the area is 0. But were we to extend one of the other two sides by an infinitesimally small amount, our area would be infinitesimally greater than 0, so presumably our minimum value is merely above zero. This means the greatest answer choice will be the number that violates the rule, and since no answer violates our minimum, (E) must again be the correct choice.
30 Nov 2014, 05:26
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pradeepss
Given two sides of a triangle, the greatest area is obtained when there is 90 degrees between them.
Thus the area cannot be more than 12*6*1/2 = 36.
Look at the diagram below:
If we consider 12 as a base, then you can see that the greatest height is when it coincides with the second side. Now, if we rotate the second side we can make the height close to zero, thus we can have any height from 0 to 6, which implies that we can have any area more than 0 but not more than 36 (12*6*1/2 = 36).
Answer: E.
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30 Nov 2014, 19:50
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area of a triangle is 1/2 a*b*sin(C)
Sin(any angle) belongs to (0,1)
so, area of traingle given= 1/2 * 6*12* Sin(C)= 36* Sin(C)
so, area must be <36
Kudos for people who got clarified with the explanation...
Sin(any angle) belongs to (0,1)
so, area of traingle given= 1/2 * 6*12* Sin(C)= 36* Sin(C)
so, area must be <36
Kudos for people who got clarified with the explanation...
