Question

Find the perimeter of triangle MNP

Answer 1

The perimeter of triangle MNP is 130 units

Explanation:

we know that

The perimeter of triangle MNP is equal to

`P=MN+NP+MP`

In this problem

step 1

1)
`MP=2(QR)`

Because Q is the midpoint of segment MN and R is the midpoint of segment NP

so

`MP=2(25)=50\ units`

step 2

2)
`NP=2(QS)`

Because Q is the midpoint of segment MN and S is the midpoint of segment MP

so

`NP=2(22)=44\ units`

step 3

3)
`MN=2(RS)`

Because R is the midpoint of segment NP and S is the midpoint of segment MP

so

`5x-34=2(x+4)`

solve for x

`5x-34=2x+8`

`5x--2x=34+8`

`3x=42`

`x=14`

so

`MN=5(14)-34=36\ units`

step 4

Find the perimeter

`P=MN+NP+MP`

substitute the values

`P=36+44+50=130\ units`