Answer:
x=5 cm,y=12 cm
Step-by-step explanation:
We are given that
RQ=3 m
PQ=4 cm
RP=x cm
RS=13 cm
SP=y cm
We know that Pythagoras theorem
[tex](Hypotenuse)^3=(base)^2+(perpendicular\;side)^2[/tex]
In right triangle RQP
Using Pythagoras theorem
[tex]RP^2=RQ^2+PQ^2[/tex]
Substitute the values
[tex]x^2=3^2+4^2[/tex]
[tex]x^2=9+16[/tex]
[tex]x^2=25[/tex]
[tex]x=\sqrt{25}=5[/tex]cm
Now,
In triangle RPS
[tex]RS^2=RP^2+SP^2[/tex]
[tex](13)^2=5^2+y^2[/tex]
[tex]169=25+y^2[/tex]
[tex]169-25=y^2[/tex]
[tex]144=y^2[/tex]
[tex]y=\sqrt{144}=12[/tex] cm
