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if the length of two sides of a triangle are 6 and 8 units, which of t

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Joined: 30 Aug 2017
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if the length of two sides of a triangle are 6 and 8 units, which of t [#permalink]

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New post 07 Oct 2017, 11:41
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  45% (medium)

Question Stats:

61% (01:01) correct 39% (01:05) wrong based on 41 sessions

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if the length of two sides of a triangle are 6 and 8 units, which of the following cannot be the area of the triangle in square units ?

a) 0.01
b) 5
c) 10
d) 20
e) 25
[Reveal] Spoiler: OA

Kudos [?]: 1 [0], given: 16

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Joined: 21 Sep 2015
Posts: 24

Kudos [?]: 8 [0], given: 9

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if the length of two sides of a triangle are 6 and 8 units, which of t [#permalink]

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New post 07 Oct 2017, 17:44
This type of question..theoretically shouldn't appear on the GMAT because it's purely testing a mathematics rule and NOT intuition nor how one thinks and solves problems.

But here goes, the trick is to realize that given 3 sides of a triangle, the area of a triangle is the largest when a triangle is a RIGHT triangle. You can find detailed proof of this with Google but here's an easy analogy:

Let's say you have a triangle of side a, b and let's say we are going to use a and b to calculate the area, ignoring c. Fix a as the base and then rotate side b on either side of a (doesn't matter). You'll see that a*height/2 is maximized when b = height and this happens when a is perpendicular to b.

With that, we have 2 sides here...HEY let's use the a and b analogy! Let's assume they are perpendicular to each other..therefore the area of the maximized area triangle is 6*8/2 = 24. E is 25 => IMPOSSIBLE (is nothing!?)

[Reveal] Spoiler:
Answer: E

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Re: if the length of two sides of a triangle are 6 and 8 units, which of t [#permalink]

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New post 08 Oct 2017, 03:38
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Let the angle between these two sides be x.

Area of triangle = \(1/2 * 6 * 8 * Sin x\)
= \(24 * Sin x\)

Now value of Sin x would lie between 0-1, for angle x between 0 - 180.
So Max area would be 24.

E.
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Kudos [?]: 6 [2], given: 3

Re: if the length of two sides of a triangle are 6 and 8 units, which of t   [#permalink] 08 Oct 2017, 03:38
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