A straight line KN is drawn through the vertex K of the triangle MKP, which is perpendicular to the plane of the triangle.

A straight line KN is drawn through the vertex K of the triangle MKP, which is perpendicular to the plane of the triangle. Known MK = KP = 10cm, MP = 12cm. Find the distance from point N to line MP.

Since MK = KR = 10 cm, the KMP triangle is isosceles.

Let us construct the spacecraft height to the base of the MР, which is also the median of the CMР triangle, then AP = AM = MР / 2 = 12/2 = 6 cm.

In a right-angled triangle AРK, according to the Pythagorean theorem, AK ^ 2 = KP ^ 2 – AP ^ 2 = 100 – 36 = 64. AK = 8 cm.

The AНK triangle is rectangular, then AH2 = KH ^ 2 + AK ^ 2 = 225 + 64 = 289.

AH = 17 cm.

Answer: From point H to line MP 17 cm.