PE||NK , MP=8, MN =12, ME,=6. найтм MK, PE, NK, PMEP:PMKN

Given the following information: MP = 8 MN = 12 ME = 6

To find MK, we need to use the Pythagorean theorem. Since MN and ME are the two sides of a right triangle, we can use the theorem to find the length of the hypotenuse MK.

Using the Pythagorean theorem, we have: MK^2 = MN^2 + ME^2 MK^2 = 12^2 + 6^2 MK^2 = 144 + 36 MK^2 = 180 MK = √180 MK ≈ 13.42

Therefore, MK ≈ 13.42.

To find PE, we need the length of PM and ME is given. Since PE is the sum of PM and ME, we can calculate it.

Given: ME = 6

To find PM, we can use the fact that PN is equal to PM + MN. PN = PM + MN 8 = PM + 12 PM = 8 - 12 PM = -4

Now, we can find PE by summing PM and ME: PE = PM + ME PE = -4 + 6 PE = 2

Therefore, PE = 2.

To find NK, we can use the fact that PN is equal to NK + KN. PN = NK + KN 8 = NK + KN Since NK and KN are equal, we can write: 8 = 2NK NK = 8/2 NK = 4

Therefore, NK = 4.

Finally, PMEP:PMKN can be found by calculating the ratio of their lengths.

PMEP:PMKN = (PM + ME)/(PN + NK) PMEP:PMKN = (PM + 6)/(PN + 4)

Using the values we found earlier: PMEP:PMKN = (-4 + 6)/(8 + 4) PMEP:PMKN = 2/12 PMEP:PMKN = 1/6

Therefore, PMEP:PMKN = 1/6.