A triangle has sides of length 7 cm, 24 cm, and 25 cm. Determine if it is a right triangle and find its area.
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- #### \( x = \frac{34}{13}, y = \frac{53}{13} \)1. **A cylindrical tank with a radius of 3 meters is filled with water to a height of 5 meters. Calculate the volume of water in the tank in cubic meters.
- Substituting the given values: \( V = \pi \times 3^2 \times 5 = 45\pi \).
- Using \( \pi \approx 3.14159 \), the volume is approximately \( 45 \times 3.14159 = 141.37155 \).
- First, check if it is a right triangle using the Pythagorean theorem: \( 7^2 + 24^2 = 49 + 576 = 625 \) and \( 25^2 = 625 \).
- The area of a right triangle is \( \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 7 \times 24 = 84 \, \text{cm}^2 \).
- A train travels 300 km in 4 hours, then 150 km in 2 hours. Calculate its average speed for the entire journey.
