Answer:
The perimeter of triangle MNP is 130 units
Step-by-step explanation:
we know that
The perimeter of triangle MNP is equal to
[tex]P=MN+NP+MP[/tex]
In this problem
step 1
1) [tex]MP=2(QR)[/tex]
Because Q is the midpoint of segment MN and R is the midpoint of segment NP
so
[tex]MP=2(25)=50\ units[/tex]
step 2
2) [tex]NP=2(QS)[/tex]
Because Q is the midpoint of segment MN and S is the midpoint of segment MP
so
[tex]NP=2(22)=44\ units[/tex]
step 3
3) [tex]MN=2(RS)[/tex]
Because R is the midpoint of segment NP and S is the midpoint of segment MP
so
[tex]5x-34=2(x+4)[/tex]
solve for x
[tex]5x-34=2x+8[/tex]
[tex]5x--2x=34+8[/tex]
[tex]3x=42[/tex]
[tex]x=14[/tex]
so
[tex]MN=5(14)-34=36\ units[/tex]
step 4
Find the perimeter
[tex]P=MN+NP+MP[/tex]
substitute the values
[tex]P=36+44+50=130\ units[/tex]
