The perimeter of the larger rectangle is 2 meters
greater than twice the perimeter of the smaller
rectangle. What is the perimeter of the larger
rectangle?

  30 m

Step-by-step explanation:

The perimeter is twice the sum of the side lengths.

The perimeter of the smaller rectangle is ...

  P1 = 2((x+1) +x) = 4x +2

The perimeter of the larger rectangle is ...

  P2 = 2((3x -1) +(4x -5)) = 14x -12

The given relation is ...

  P2 = 2×P1 +2

  14x -12 = 2(4x +2) +2

  6x = 18 . . . . . . . . . . add 12-8x, simplify

  x = 3

Then the perimeter of the larger rectangle is ...

  P2 = 14(3) -12 = 30

The perimeter of the larger rectangle is 30 meters.

Check

  P1 = 4(3) +2 = 14

  2(14) +2 = 28 +2 = 30 . . . . satisfies the relation between perimeters

step-by-step explanation:

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