2. the length of a rectangle is 5 mm longer than its width. its perimeter is more than 30 mm. let w equal the width of the rectangle. (a) write an expression for the length in terms of the width. (b) use expressions for the length and width to write an inequality for the perimeter, on the basis of the given information. (c) solve the inequality, clearly indicating the width of the rectangle.

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 to get > 30 as we are given the perimeter. However, we know that the length of the of the rectangle is 5mm longer than its width, which will make them x+5 units long. So, our equation is:
x+(x+5)+x+(x+5) > 30
where x is a measure of the width and (x+5) is a measure of the length. Now we solve, first collecting the like terms:
x+x+5+x+x+5 > 30
4x+10 > 30
Now minus 10 on both sides:
4x > 20
And finally divide by 4 on both sides to isolate x:
x > 5
So the width (x) greater than 5mm, and the length (x+5) is greater than 10mm.

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