Remember geometry and use your imagination to find the correct answer.
In 1995, eighth graders from 16 countries took the TIMSS test, which was used to evaluate the quality of school mathematics education. One of the tasks seemed especially difficult to the students: only 10% managed it. Check if it's up to you.
A string is wound symmetrically around a round rod. She makes exactly 4 turns around it. The length of the rod is 12 centimeters and its circumference is 4 centimeters. What is the length of the string?
Image: Anna Guridova/TricksHelper
Let's imagine that the rod is cardboard. If you cut it lengthwise in a straight line, and then unfold and flatten it, you will get a rectangle measuring 12 × 4 cm. The wound string will turn into 4 diagonal lines, each of which is the hypotenuse of a right triangle.
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Image: Anna Guridova/TricksHelper
The length of one of the legs of these right triangles is equal to the length the circumference of the rod, that is, 4 cm. The length of the other leg is one-fourth the length of the rod, that is, 12 ÷ 4 = 3 cm.
To find the hypotenuse, you need to use the Pythagorean theorem. It sounds like this: in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the legs.
Let's calculate the square of the hypotenuse: 32 + 42 = 9 + 16 = 25. This means the length of the hypotenuse is √25 = 5 cm. Therefore, the total length of the string is equal to the sum of 4 hypotenuses, that is, 20 cm.
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The original problem can be viewed here.
