The length of a rectangle is 8 more than the width. the perimeter of the rectangle is 56 inches. write and solve a system of linear equations to find the length and width of the rectangle. show and explain each step thoroughly.

There are 4 sides to a rectangle, which we will name as x as we do not know their length yet. We will be adding up these 4 sides as we are given the perimeter. However, we know that the length of the of the rectangle is 8 units longer than its width, which will make them x+8 units long. So, our equation is:
x+(x+8)+x+(x+8)=56
where x is a measure of the width and (x+8) is a measure of the length. Now we solve, first collecting the like terms:
x+x+8+x+x+8=56
4x+16=56
Now minus 16 on both sides:
4x=40
And finally divide by 4 on both sides to isolate x:
x=10
So, the width (x) is 10 units, and the length (x+8) is 12 units.

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