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 IIIIII. 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
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