9514 1404 393
Answer:
x = 12
perimeter = 124
Step-by-step explanation:
The midline RS is half the length of MN, so we have ...
2×RS = MN
2(x +3) = 5x -30
2x +6 = 5x -30
36 = 3x . . . . . . . . . add 30-2x
12 = x . . . . . . . . . . divide by 3
__
The length RS is then ...
RS = x +3 = 15
and the perimeter of QRS is ...
P(QRS) = QR +RS +SQ = 25 +15 +22 = 62
The perimeter of QRS is half the perimeter of MNP, so ...
P(MNP) = 2×P(QRS) = 2×62 = 124
The perimeter of ΔMNP = 124.
