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Re: The width, length, and diagonal of a rectangle could be represented by [#permalink]

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20 Nov 2015, 01:04

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
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The width, length, and diagonal of a rectangle could be represented by which of the following groups of numbers?

I. 2, 3, \(\sqrt{13}\) II. \(\sqrt{10}\), 4, 6 III. 3, 10, 11

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

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

Re: The width, length, and diagonal of a rectangle could be represented by [#permalink]

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22 Nov 2015, 02:41

The width, length, and diagonal of a rectangle could be represented by which of the following groups of numbers?

I. 2, 3, 13‾‾‾√ II. 10‾‾‾√, 4, 6 III. 3, 10, 11

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

The Three dimensions of a rectangle in the given order represents the two side and the hypotenuse of a right angle trianlge. Only set that obeys pythogerous theorem is I. So Ans: A