2024 Author: Malcolm Clapton | [email protected]. Last modified: 2023-12-17 03:44
Remember geometry and use your imagination to find the right answer.
In 1995, eighth graders from 16 countries took the TIMSS test, which was used to assess the quality of school mathematics education. One of the tasks seemed especially difficult to the students: only 10% of Mathematics and Science Achievement in the Final Year of Secondary School coped with it. Check if she's in your teeth.
A string is symmetrically wound on a round rod. She makes exactly 4 turns around him. The rod is 12 centimeters long and its circumference is 4 centimeters. What is the length of the string?
Let's imagine that the rod is made of cardboard. If you cut it along in a straight line, and then unfold and flatten it, you get a 12 × 4 cm rectangle. The wound string will turn into 4 diagonal lines, each of which is the hypotenuse of a right triangle.
Image: Anna Guridova / Lifehacker
The length of one of the legs of these right-angled triangles is equal to the circumference of the rod, that is, 4 cm. The length of the other leg is one-fourth of 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-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the legs.
Calculate the square of the hypotenuse: 32 + 42 = 9 + 16 = 25. Hence, 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.
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