The triangle ΔPNR is formed by the segment PR drawn
parallel to the side MK.
Correct response:
Given;
ΔMNK = A right triangle
MK = 12
NK = 15
Midpoint of MN = P
PR ║ MK
Required:
The perimeter of ΔPNR
Solution:
∠KMN = ∠RPN = 90° (definition of parallel lines PR and MK)
ΔPNR is a right triangle by definition
From Pythagorean theorem, we have;
MN = √(15² - 12²) = 9
[tex]PN = \dfrac{MN}{2}[/tex], by definition of midpoint
Therefore;
[tex]PN = \dfrac{9}{2} = \mathbf{4.5}[/tex]
MP = PN = 4.5
[tex]\dfrac{KR}{RN} = \dfrac{MP}{PN} = \dfrac{4.5}{4.5} = 1[/tex], by triangle proportionality
Therefore;
KR = RN
KR + RN = NK = 15 segment addition postulate
2·RN = 15 by substitution property
[tex]RN = \dfrac{15}{2} = 7.5[/tex]
RP = √(7.5² - 4.5²) = 6
The perimeter of ΔPNR = PN + RN + RP
Which gives;
Perimeter of ΔPNR = 4.5 + 7.5 + 6 = 18
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