The segment MH intersects a certain plane at point K. Through the ends of the segment, straight lines
| September 26, 2021 | education
The segment MH intersects a certain plane at point K. Through the ends of the segment, straight lines HP and ME are drawn, perpendicular to the plane and intersecting it at points P and E. Find PE if HP = 4 cm, HK = 5 cm, ME = 12 cm.
The angles MKE and NKP are equal, since they are formed by intersecting straight lines. Hence the equality is also true: NP / NK = ME / MK.
Find segment MK:
MK = (5 * 12) / 4 = 15.
By the Pythagorean theorem, we find the segments KP and KE.
KP ^ = KN ^ – NP ^ = 25 – 16 = 9.
KP = 3.
KE ^ = MK ^ – ME ^ = 225 – 144 = 81.
KE = 9.
Find PE:
PE = KE + KP = 9 + 3 = 12.
Answer: PE = 12.
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