Answer:
- NE = 7.5 units
- GO = 9 units
- AG = 12 units
- perimeter = 36 units
Step-by-step explanation:
OA is twice the length of midsegment NE.
4x +3 = 2(2.5x)
3 = x . . . . . . . . . . subtract 4x
The length of NE is 2.5(3) = 7.5 units.
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Similarly, GO is twice the length of RN.
The length of GO is 2(4.5) = 9 units.
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ER is 2(3) = 6, and AG is twice that length. AG = 2(6) = 12 units.
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OA is twice the length of NE, so is 2(7.5) = 15 units. The perimeter of the triangle is ...
P = OA +AG +GO = 15 +12 +9 = 36 units
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- NE = 7.5 units
- GO = 9 units
- AG = 12 units
- perimeter = 36 units
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Additional comment
The side lengths of triangle OAG have the ratios 9 : 12 : 15 = 3 : 4 : 5. You may recognize these ratios as belonging to a right triangle. The right angle is at vertex G, opposite the longest side, OA.
