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17 May 2016, 03:42
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D
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Difficulty:
85%
(hard)
Question Stats:
36% (01:23) correct
64%
(02:14)
wrong
based on 171
sessions
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One side of a triangle has length 8 and a second side has length 5. Which of the following could be the area of the triangle?
I. 24
II. 20
III. 5
A. I only
B. II only
C. III only
D. II and III only
E. I, II and III
I. 24
II. 20
III. 5
A. I only
B. II only
C. III only
D. II and III only
E. I, II and III
17 May 2016, 10:43
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The triangle will have a maximum area when it is a right angled triangle
The largest triangle will be formed when 8 and 5 are the base and height of triangle .
Area = 1/2 * 8 * 5 = 20
There is no lower limit on the area of any triangle whose only 2 sides are known . Area> 0
So we can also have triangle with area = 5
Suppose we want to take 8 as the hypotenuse in the right angled triangle , then one of the other sides(base or height) will be less than 8 .
Hence , product will be lesser than 20 .
Answer D
The largest triangle will be formed when 8 and 5 are the base and height of triangle .
Area = 1/2 * 8 * 5 = 20
There is no lower limit on the area of any triangle whose only 2 sides are known . Area> 0
So we can also have triangle with area = 5
Suppose we want to take 8 as the hypotenuse in the right angled triangle , then one of the other sides(base or height) will be less than 8 .
Hence , product will be lesser than 20 .
Answer D
General Discussion
17 May 2016, 11:06
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I agree D too. Taking it that the 2 possible largest sides to calculate area of triangle are 5 and 8 then (8x5/2 = 20).
One could also try the validity of 5 by assuming that 8 is the hypothenuse so a^2 +b^2 = c^2 would look something like a^2+5^2 = 8^2 and thus a must be an estimate of 6~ assuming we use 6 then 6*5=30/2 = 15 and thus assuming that any answer below 20 is possible is correct!
One could also try the validity of 5 by assuming that 8 is the hypothenuse so a^2 +b^2 = c^2 would look something like a^2+5^2 = 8^2 and thus a must be an estimate of 6~ assuming we use 6 then 6*5=30/2 = 15 and thus assuming that any answer below 20 is possible is correct!
