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Is area of the triangle ABC greater than 24? 1) Two of the Sides of t

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Is area of the triangle ABC greater than 24? 1) Two of the Sides of t  [#permalink]

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03 Jul 2018, 05:50
00:00

Difficulty:

75% (hard)

Question Stats:

40% (01:20) correct 60% (01:30) wrong based on 28 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

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Is area of the triangle ABC greater than 24? 1) Two of the Sides of t  [#permalink]

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03 Jul 2018, 07:54
GMATinsight wrote:
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: http://www.GMATinsight.com

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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Is area of the triangle ABC greater than 24? 1) Two of the Sides of t &nbs [#permalink] 03 Jul 2018, 07:54
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