The height of a right-angled triangle, drawn to the hypotenuse, divides it into segments
| July 13, 2021 | education
The height of a right-angled triangle, drawn to the hypotenuse, divides it into segments, the lengths of which are 9k 1. If the height is 6, then the hypotenuse is?
Let the segment CH of the hypotenuse AC be equal to X cm, then, by condition, the segment AH = 9 * X cm.
From the property of the height of a right-angled triangle drawn from the apex of an obtuse angle, we determine the height of the HV.
BH2 = AH * CH.
36 = 9 * X * X = 9 * X2.
X ^ 2 = 36/9 = 4.
X = 2 cm.
CH = 2 cm.
AH = 9 * CH = 9 * 2 = 18 cm.
Let us determine the length of the AC hypotenuse.
AC = CH + AH = 2 + 18 = 20 cm.
Answer: The length of the hypotenuse is 20 cm.
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