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03 Jul 2018, 06:50
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A
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:
37% (01:11) correct
63%
(01:39)
wrong
based on 51
sessions
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Is area of the triangle ABC greater than 24?
1) Two of the Sides of the triangle are 6 and 8
2) ABC is a Right Triangle.
Source: www.GMATinsight.com
1) Two of the Sides of the triangle are 6 and 8
2) ABC is a Right Triangle.
Source: www.GMATinsight.com
03 Jul 2018, 08:54
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GMATinsight
Statement 1:-
Let the length of the 3rd side of given triangle ABC is x unit.
Property-I
Given Two sides of a triangle, the greatest area is obtained when there is a 90 degree between them.
Thus, area is maximum when ABC is a right angled triangle, so x=10 unit (Pythagorean triplet:- 6,8,10)
So, max. area=24 sq unit. So, answer to the question stem is No.
Property-II
"The length of any side of a triangle must be larger than the positive difference of the other two sides, but smaller than the sum of the other two sides."
Given the length of two sides are 6 and 8 units, thus, we have
2<x<14.
From property-I, we have max. area at x=10.
hence, any measure of x between 2 to 14(both exclusive) will yield an area less than 24 except at x=8, with fixed measure of the other two sides(6 and 8 units)
Our answer to the question stem is No.
Therefore st1 is sufficient.
Statement-2:-
ABC is a Right Triangle. No information on the measure of sides are provided.
hence we can't definitely say about the measure of area.
Ans. (A)
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