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The perimeter of the triangle is 8x + 4y. The measures of two of the sides are x + 2y and 3x + y. If these two sides were added together, they would be 4x + 3y:

x + 2y

3x + y

4x + 3y

The third side is the perimeter minus the two known sides, so 8x + 4y - (4x + 3y). Distribute the negative: 8x + 4y - 4x - 3y. This is equal to the third side, which is 4x +y.

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