The height drawn from the top of the obtuse corner of the rhombus divides the opposite side into 6 cm and 4

| August 11, 2021 | education

The height drawn from the top of the obtuse corner of the rhombus divides the opposite side into 6 cm and 4 cm segments starting from the top of the acute angle. find the length of the height of the rhombus.

Let us determine the length of the side of the specified rhombus, knowing by the condition of the problem that it is divided by its height into two segments, with the length of the first of them equal to 6 centimeters and the length of the second equal to 4 centimeters:

6 + 4 = 10.

Since the drawn height forms a right-angled triangle with one of the resulting segments and the other side of the rhombus, we compose an equation according to the Pythagorean theorem and determine the length of the height of the rhombus (taking it for x):

x ^ 2 + 6 ^ 2 = 10 ^ 2;

x ^ 2 = 64;

x1 = 8;

x2 = -8.

Answer: The length of the height of the rhombus is 8 centimeters.



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