In a right-angled triangle with legs 3 and 4, the height is lowered by the hypotenuse.

univerkov | February 22, 2021 | education

In a right-angled triangle with legs 3 and 4, the height is lowered by the hypotenuse. Find this height and the segments into which it divides the hypotenuse.

1. A, B, C – the vertices of the triangle. S – area. CE – height. ∠С = 90 °.

2. AB = √AC² + BC² (by the Pythagorean theorem).

AB = √4² + 3² = √25 = 5 units.

3. S = AC x BC / 2 = 4 x 3/2 = 6 units².

4. According to another formula S = AB x CE / 2.

CE = 2S: AB = 2 x 6: 5 = 2.4 units.

5. BE = √BC² – CE² = √9² – 2.4² = √3.24 = 1.8 units.

6. AE = 5 – 1.8 = 3.2 units.

Answer: height CE, segments AE and BE are equal to 5, 3.2, 1.8 units of measurement, respectively.

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