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

**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.