9514 1404 393
Answer:
x = 6.0 cm
Explanation:
The ratio of the given dimensions is 2.5/6.5 = 5/13. This should give you a clue that the dimensions here are all half those of the (5, 12, 13) Pythagorean triple. That is, ...
x = 12/2 = 6 . . . cm
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In case you haven't memorized a few of the Pythagorean triples commonly used in algebra problems*, you can figure x using the Pythagorean theorem:
6.5² = 2.5² +x²
42.25 -6.25 = x²
x = √36 = 6
x = 6.0 cm
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* most commonly seen are (3, 4, 5), (5, 12, 13), (7, 40, 41) and their multiples.