The height, drawn to the hypotenuse of a right-angled triangle, divides it into segments 9 cm
| April 26, 2021 | education
The height, drawn to the hypotenuse of a right-angled triangle, divides it into segments 9 cm and 16 cm long. Find: Larger leg.
Height AD is drawn to the hypotenuse from the top of the right angle, then AD ^ 2 = BD * CD = 16 * 9 = 144.
AD = 12 cm. In a right-angled triangle ABD, according to the Pythagorean theorem, we determine the length of the hypotenuse AB.
AB ^ 2 = AD ^ 2 + BD ^ 2 = 144 + 256 = 400.
AB = 20 cm.
Answer: The length of the larger leg is 20 cm.
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