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# The width, length, and diagonal of a rectangle could be represented by

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

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20 Nov 2015, 00:48
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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
[Reveal] Spoiler: OA

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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.

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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, 19:41
1. 2, 3, sqrt(13)
squaring all numbers: 4, 9 , 13
since third number is sum of other 2: 4+9 = 13

2. sqrt(10), 4, 6
squaring all numbers: 16, 36 , 10
since third number is not the sum of other 2: 16+10 = 26 which is not equal to 36
Not possible

3.3, 10 , 11
squaring all numbers: 9, 100 , 110
since third number is not the sum of other 2: 100+9 = 109 which is not equal to 110
Not possible

Ans: A

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

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21 Nov 2015, 15:15
Bunuel wrote:
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

Cheers,
Brent
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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

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Re: The width, length, and diagonal of a rectangle could be represented by   [#permalink] 22 Nov 2015, 02:41
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# The width, length, and diagonal of a rectangle could be represented by

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