the perimeter of a rectangle is 34cm. the length is 1cm longer than the width. What are the dimensions of the reactangle? show your work

Let W be the width of the rectangle.

Let L be the length of the rectangle.

The length is 3 cm more than twice its width. Therefore:

L = 2W + 3

The perimeter of the rectangle is 34 cm. Therefore:

2W + 2L = 34

We can substitute the value of L from the first equation into the second:

2W + 2 (2W + 3) = 34

Distributing the 2 on the right:

2W + 2*2W + 2*3 = 34

2W + 4W + 6 = 34

6W + 6 = 34

Subtracting 6 from both sides:

6W + 6 - 6 = 34 - 6

6W = 28

Dividing both sides by 6:

or,

W = 4 and 2/3

We can substitute this value of W back into the first equation

to find the value of L:

L = 2*W + 3

or,

L = 9 and 1/3 + 3 so,

L = 12 and 1/3