Answer:
Option 4 is correct. The length of PR is 6.4 units.
Step-by-step explanation:
From the given figure it is noticed that the triangle PQR and triangle MQR.
Let the length of PR be x.
Pythagoras formula
[tex]hypotenuse^2=base^2+perpendicular^2[/tex]
Use pythagoras formula for triangle PQM.
[tex]PM^2=QM^2+PQ^2[/tex]
[tex]PM^2=(6)^2+(8)^2[/tex]
[tex]PM^2=36+64[/tex]
[tex]PM^2=100[/tex]
[tex]PM=10[/tex]
The value of PM is 10. The length of PR is x, so the length of MR is (10-x).
Use pythagoras formula for triangle PQR.
[tex]PQ^2=QR^2+PR^2[/tex]
[tex](8)^2=QR^2+x^2[/tex]
[tex]64-x^2=QR^2[/tex] .....(1)
Use pythagoras formula for triangle MQR.
[tex]MQ^2=QR^2+MR^2[/tex]
[tex](6)^2=QR^2+(10-x)^2[/tex]
[tex]36=QR^2+x^2-20x+100[/tex]
[tex]36-x^2+20x-100=QR^2[/tex] .... (2)
From equation (1) and (2) we get
[tex]36-x^2+20x-100=64-x^2[/tex]
[tex]20x-64=64[/tex]
[tex]20x=128[/tex]
[tex]x=6.4[/tex]
Therefore length of PR is 6.4 units and option 4 is correct.
