Through the point O of the intersection of the diagonals of the rhombus to its plane, a perpendicular

| September 21, 2021 | education

Through the point O of the intersection of the diagonals of the rhombus to its plane, a perpendicular OK 5 cm long is drawn. Find the distance from point K to each side if the diagonals of the rhombus are 40 cm and 30 cm.

The diagonals of the rhombus, at the point of intersection, are divided in half, AO = CO = AC / 2 = 40/2 = 20 cm,

BO = DO = BD / 2 = 30/2 = 15 s.

By the Pythagorean theorem, we determine the length of the side of the rhombus. AD ^ 2 = AO ^ 2 + DO ^ 2 = 400 + 225 = 625.

AD = DC = BC = AB = 25 cm.

Consider a triangle COD, whose OM is the height of the triangle.

Determine the area of ​​the triangle COD.

Sod = (OD * OS) / 2 = 15 * 20/2 = 150 cm2.

Let’s use the area formula in terms of the height of the triangle.

Sod = (ОМ * СD) / 2 = ОМ * 25/2.

Let’s equate the area.

ОМ * 25/2 = 150.

OM = 150 * 2/25 = 12 cm.

Consider a right-angled triangle KOM and define the hypotenuse KM.

KM ^ 2 = OK ^ 2 + OM ^ 2 = 25 + 144 = 169.

KM = 13 cm.

Answer: The distance from point K to each side is 13 cm.



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