If two sides of a triangle have lengths 3.2 and 5.4 then the length of

Question

If two sides of a triangle have lengths 3.2 and 5.4 then the length of the third side must be between

(A) 0.0 and 2.2
(B) 2.2 and 5.4
(C) 2.2 and 8.6
(D) 3.2 and 5.4
(E) 5.4 and 8.6

KakashiSensei · Answer

sum of 2 sides > third side
difference of 2 sides < third side
Hence C.

unraveled · Answer

Possibilities: 
1. 5.4 is largest side
1a. 3.2 is medium side.
Smallest side > 5.4 - 3.2(2.2)
Only B and C are contenders.

1b. 3.2 is smallest of the sides
Then 
3.2 < medium side < 5.4

2. 5.4 is medium side with 3.2 as smallest.
Largest side < 5.4 + 3.2(8.6)

Answer C.

MathRevolution · Answer

Third side: x => (5.4 - 3.2) < x < (5.4 + 3.2) => 2.2 < x < 8.6 Answer C

CrackverbalGMAT · Answer

Solution:

To solve this question, we have to use the fundamental properties of a triangle with sides a,b,c that

(1)The sum of two sides of a triangle is less than the third side and a + b < c => c > a + b

(2)The difference of two sides of a triangle is more than the third side a- b >c => c < a - b

Here a = 5.4 b=3.2 and hence c > 5.4 + 3.2 = 8.6 and

c < 5.4 - 3.2 = 2.2

=> 2.2 < c < 8.6 (option c)

Devmitra Sen
GMAT SME

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If two sides of a triangle have lengths 3.2 and 5.4 then the length of

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