The width, length, and diagonal of a rectangle will be Pythagorean triples .
(width)^2 + (length)^2 = (diagonal)^2

1. 2^2 + 3^2 = (13^(1/2))^2 = 13
=> 4+9 = 13
Yes.
2.
(10^(1/2))^2 + 4^2 = 10 + 16 = 26
which is not equal to 6^2= 36
No.
3. 3^2 + 10^2 = 9 +100 = 109
not equal to 11^2 = 121
No.

Answer A
_________________

NOTE: The width, length, and diagonal create a RIGHT TRIANGLE, with the diagonal as the hypotenuse.
For these to be valid lengths, the Pythagorean Theorem must apply.
That is, it MUST be the case that width² + length² = diagonal²

Let's check the 3 sets of values BEGINNING WITH III

III. Does 3² + 10² = 11²? NO.
This means that 3, 10, 11 CANNOT represent the width, length, and diagonal of a rectangle.
This means we can ELIMINATE C, D and E

II. Does (√10)² + 4² = 6²? NO.
This means that √10, 4, 6 CANNOT represent the width, length, and diagonal of a rectangle.
This means we can ELIMINATE B

Answer: A

Cheers,
Brent
_________________

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________