1) A rectangle has the lengths shown
Find the perimeter of the rectangle.

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Find the perimeter by solving for y.

We know that a rectangle contains two pairs of parallel and congruent sides, therefore:

5y - 1 = 2y + 8

We can solve for y using this expression. Begin by subtracting 2y from both sides:

5y - 2y - 1 = 2y - 2y + 8

3y - 1 = 8

Add 1 to both sides:

3y - 1 + 1 = 8 + 1

3y = 9

Divide both sides by 3:

y = 3

Recall that the perimeter of a rectangle is:

P = 2l + 2w

Plug in the given expressions for the side lengths to find one equation:

P = 2(5y - 1) + 2(y - 1)

Simplify by distribution:

P = 10y - 2 + 2y - 2

Combine like terms:

P = 12y - 4

Plug in the solved value of y into this equation:

P = 12(3) - 4

P = 36 - 4

P = 32 cm.

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