5
QuizMultiple Choice

Converse to the Pythagorean Theorem — Quiz

Question 5 • Foundations of Math 1

Jackie plans to place a rectangular piece of art inside a rectangular frame. She considers a piece of art that is 0 point 5 meters long, 1 point 2 meters wide, and has a diagonal length of 1 point 3 meters. Which is true regarding the art piece?

Answer
A
The art is not rectangular because 0 point 5 squared plus 1 point 2 squared is not equal to 1 point 3 squared .
B
The art is rectangular because 1 point 2 squared minus 0 point 5 squared is less than 1 point 3 squared .
C
The art is rectangular because 0 point 5 squared plus 1 point 2 squared is equal to 1 point 3 squared .
D
The art is not rectangular because 0 point 5 squared plus 1 point 2 squared is greater than 1 point 3 squared .

Explanation

For a rectangle, the side lengths and diagonal form a right triangle, so the Pythagorean theorem must hold: length² + width² = diagonal². Here, 0.5² + 1.2² = 0.25 + 1.44 = 1.69, and 1.3² = 1.69. Therefore, the art is rectangular, as stated in choice C.

AI-written and checked against the verified answer.

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