In the rhombus ABCD, AB = 10cm, BD = 12cm, the line MC is perpendicular to the rhombus
| August 9, 2021 | education
In the rhombus ABCD, AB = 10cm, BD = 12cm, the line MC is perpendicular to the rhombus, find AM if tM is 16 cm away from the rhombus.
The diagonals of the rhombus intersect at right angles and at the point of intersection are divided in half, then BO = BD / 2 = 12/2 = 6 cm, and triangle ABO is rectangular.
In the triangle ABO, according to the Pythagorean theorem, we determine the length of the leg AO. AO ^ 2 = AB ^ 2 – BO ^ 2 = 10 ^ 2 – 6 ^ 2 = 100 – 36 = 64.
AO = 8 cm, then the diagonal AC = 2 * AO = 2 * 8 = 16 cm.
In a right-angled triangle ACM, according to the Pythagorean theorem, we determine the length of the hypotenuse AM.
AM ^ 2 = AC ^ 2 + CM ^ 2 = 16 ^ 2 + 16 ^ 2 = 256 + 256 = 512.
AM = 16 * √2 cm.
Answer: The segment AM = 16 * √2 cm.
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