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.

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step-by-step explanation: