Answer:
- MN = 68
- MO = 76
- ON = 68
- perimeter = 212
Step-by-step explanation:
You have ∆MNO with ∠M≅∠O and sides MN = 22x+24, MO = 6x+64, ON = 10x+48. You want the length of each side, and the perimeter.
Side lengths
Angles M and O being congruent means that sides ON and MN are congruent:
ON = MN
10x +48 = 22x +24
24 = 12x . . . . . . . . . . . subtract 10x+24
2 = x . . . . . . . . . . divide by 12
Then the side lengths are ...
ON = MN = 10x +48 = 10(2) +48 = 68
MO = 6x +64 = 6(2) +64 = 76
Perimeter
The perimeter is the sum of the side lengths:
ON +MN +MO = 68 +68 +76 = 212
The side lengths and perimeter are ...
- MN = 68
- MO = 76
- ON = 68
- perimeter = 212.
