Through the point O of the intersection of the diagonals of the square ABCD, a perpendicular MO

| July 29, 2021 | education

Through the point O of the intersection of the diagonals of the square ABCD, a perpendicular MO with a length of 15 cm is drawn to its plane.Find the distance from point M to the sides of the square if its side is 16 cm.

The diagonals of the square, when crossed, form four isosceles right triangles.

Let’s draw the height OH of the right-angled and isosceles triangle AOB. The height OH is also the bisector and median of the triangle. AH = BH = AB / 2 = 16/2 = 8 cm.

In the triangle AHO, the angle H = 90, and the angle A and O are equal to 45, then the triangle AHO is also isosceles and rectangular, AH = OH = 8 cm.

In a right-angled triangle MOH, we define, applying the Pythagorean theorem, the hypotenuse MH.

MH ^ 2 = MO ^ 2 + MH ^ 2 = 225 + 64 = 289.

MH = 17 cm.

Answer: The distance from point M to the sides of the square is 17 cm.



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