The rectangle shown has a perimeter of 102 cm and the given area. its length is 6 more than four times four times its width. write and solve a system of equations to find the dimensions of the rectangle.

The rectangle has two sides of length L and two sides of length W. The perimeter of the rectangle is the addition of all sides.

P = 2L + 2W

We are told the length is 6 more than 4 times its width. Therefore, we can write:

L = 4W + 6

We know the perimeter, and we can now substitute L into the perimeter equation and solve for W.

2L + 2W = P
2(4W + 6) + 2W = 102
6W + 12 + 2W = 102
8W = 90
W = 11.25 cm

We have solved the width as 11.25 cm and can now solve for the length.

L = 4W + 6
L = 4(11.25) + 6
L = 45 + 6
L = 51 cm

The length of the rectangle is 51 cm, the width of the rectangle is 11.25 cm.