The diagonal of the rhombus is 60 and 80 cm of the intersection point of the diagonal of the plane

| May 14, 2021 | education

The diagonal of the rhombus is 60 and 80 cm of the intersection point of the diagonal of the plane of the rhombus, a perpendicular 45 cm long is drawn, find the distance from this point to the side of the rhombus.

In a rhombus, the diagonals at the intersection point are divided in half, then AO = CO = AC / 2 = 80/2 = 40 cm, BO = DO = BD / 2 = 60/2 = 30 cm.

In a right-angled triangle COD, according to the Pythagorean theorem, we define the hypotenuse CD, which is the side of the rhombus.

CD ^ 2 = CO ^ 2 – DO ^ 2 = 1600 + 900 = 250.

CD = 50 cm.

Knowing the lengths of all sides of the COD triangle, we determine its area through a semi-perimeter.

p = (OC + OD + CD) / 2 = (30 + 40 + 50) / 2 = 60 cm.

Then Sos = √р * (р – OS) * (р – ОD) * (р – СD) = √60 * 30 * 40 * 50 = √360000 = 600 cm2.

The area of ​​a triangle can also be determined through the height and base.

Sosd = СD * ОМ / 2 = 50 * ОМ / 2 = 60.

ОМ = 1200/50 = 24 cm.

From the right-angled triangle KOM, we determine the length of the hypotenuse KM.

KM ^ 2 = OM ^ 2 + OK ^ 2 = 24 ^ 2 + 45 ^ 2 = 576 + 2025 = 2601.

KM = 51 cm.

Answer: The distance is 51 cm.



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