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Triangle

by sumanr84 » Sun Jul 11, 2010 4:20 am
If the lengths of the sides of a triangle are a , b , and 7, which of the following could be the value of a - b ?

I. 4
II. 7
III. 12

A. I only
B. II only
C. I and II only
D. II and III only
E. I, II, and III

[spoiler]Source : Kaplan Cat, OA : A[/spoiler]
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by Rahul@gurome » Sun Jul 11, 2010 4:31 am
We know that sum of 2 sides of a triangle is greater than the 3rd side. So, b+7 > a implies a - b < 7
Similarly, a + 7 > b implies a - b > -7

Combining both the above inequalities, we get -7 < (a - b) < 7 that is a - b lies between -7 and 7.

From the options I, II & III, the only possible option is I i.e a - b can take the value 4.

The correct answer is (A).
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by selango » Sun Jul 11, 2010 9:28 am
1.Sum of 2 sides of triangle is greater than third side.

2.Difference between 2 sides of triangle is greater than third side.

Let third side be 7

a-b<7<a+b

So a-b<7

Only option A satisfy this inequality.
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