Answer:
PR = 17 cm
Step-by-step explanation:
Given :
In ΔPQR,
PQ = 39 cm
PN is an altitude.
QN = 36 cm
RN = 8 cm.
To Find : Length of PR
Solution :
Since we are given that PN is an altitude .
So, PN divides ΔPQR in two right angled triangles named as ΔPQN and ΔPRN. (Refer attached file)
So, first we find Length of PN in ΔPQN using Pythagoras theorem i.e.
[tex](Hypotenuse)^{2}=(Perpendicular)^{2} +(Base)^{2}[/tex]
[tex](PQ)^{2}=(PN)^{2} +(QN)^{2}[/tex]
[tex](39)^{2}=(PN)^{2} +(36)^{2}[/tex]
[tex]1521=(PN)^{2} +1296[/tex]
[tex]1521 -1296=(PN)^{2} [/tex]
[tex]225=(PN)^{2} [/tex]
[tex]\sqrt{225} = PN[/tex]
[tex]15 = PN[/tex]
Thus, Length of PN = 15cm
Now to find length of PR we will use Pythagoras theorem in ΔPRN.
[tex](PR)^{2}=(PN)^{2} +(NR)^{2}[/tex]
[tex](PR)^{2}=(15)^{2} +(8)^{2}[/tex]
[tex](PR)^{2}=225 +64[/tex]
[tex](PR)^{2}=289[/tex]
[tex] PR= \sqrt{289} [/tex]
[tex] PR= 17 [/tex]
Hence the length of PR = 17 cm
