The rectangle shown has a perimeter of 44 cm and the given area. Its length is 7 more than twice its width. Write and solve a system of equations to find the dimensions of the rectangle.

The length of the rectangle is __ cm and the width of the rectangle is __ cm

The length of the rectangle is 17 cm and the width of the rectangle is 5 cm.

Step-by-step explanation:

Given the measurements in the question, you can set up two different equations to find the length and width of the rectangle. First, the formula for the perimeter of a rectangle is: P = 2W + 2L, where W = width and L=length. In this problem the L is '7 more than twice its width', this means our first equation is:

L = 2W + 7

Next, we can use this expression in our formula for perimeter to get our second equation:

P = 2W + 2 (2W + 7) or 44 = 2W + 2 (2W + 7)

Distribute: 44 = 2W + 4W + 14

Combine like terms: 44 = 6W + 14

Subtract 14 from both sides: 44 - 14 = 6W + 14 - 14 or 30 = 6W

Divide 6 from both sides: 30/6 = 6W/6 or W = 5

Now, solve for L: L = 2 (5) + 7 or L = 10 + 7 = 17

So, the width is 5cm and the length is 17 cm.