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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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Intern
Joined: 30 Aug 2017
Posts: 15
if the length of two sides of a triangle are 6 and 8 units, which of t  [#permalink]

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07 Oct 2017, 11:41
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Difficulty:

45% (medium)

Question Stats:

56% (01:23) correct 44% (01:41) wrong based on 59 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
Manager
Joined: 21 Sep 2015
Posts: 57
if the length of two sides of a triangle are 6 and 8 units, which of t  [#permalink]

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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!?)

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Insanity at its finest.

Intern
Joined: 28 Dec 2010
Posts: 49
Re: if the length of two sides of a triangle are 6 and 8 units, which of t  [#permalink]

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08 Oct 2017, 03:38
3
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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Re: if the length of two sides of a triangle are 6 and 8 units, which of t &nbs [#permalink] 08 Oct 2017, 03:38
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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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