Problem 6 of 34geo-006
A square has sides that are each centimeters long. What is the length, in centimeters, of a diagonal of the square?
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Solution walkthrough1:41
- A diagonal cuts the square into two right triangles. The legs are sides of the square, so both are .
- Two equal legs make a 45-45-90 triangle. Its sides are always , and .
- Here each leg is , so the hypotenuse, the diagonal, is .
- Check with the Pythagorean theorem: , and .
- Traps: is , adds the two sides, and borrows from the 30-60-90 triangle.