A triangle has sides of lengths 7 cm, 24 cm, and 25 cm. Is it a right triangle? If so, find the area.
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- Using the principle of inclusion-exclusion:
- Number playing at least one sport \(= 18 + 12 - 5 = 25\).
- Number playing neither \(= 30 - 25 = 5\).
- Check using Pythagorean theorem: \(7^2 + 24^2 = 49 + 576 = 625 = 25^2\).
- Area \(= \frac{1}{2} \times 7 \times 24 = 84\) square cm.
- Solve for \(x\): \(2^{x+1} = 32\).
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