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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Rahul@gurome
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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).
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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selango
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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.
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.
--Anand--
