a rectangular suitcase measure 24 inches long and the diagonal is 30 inches long. the zipper covers the entire perimeter of the suitcase. how many inches of the zipper was needed to cover the perimeter of the suitcase?

Given parameters:

Length of the suitcase  = 24 inches

Length of the diagonal = 30 inches

Unknown:

Length of zipper required to cover the perimeter  = ?

The length of this zipper is the same as the perimeter of the rectangular suitcase.

  Perimeter of a rectangle  = 2(L + B)

where L is the length and B is the breadth

Now, let us find the find the unknown breadth;

  Using Pythagoras theorem;

           30²  = 24² + Breadth²

            Breadth²  = 30² - 24²  = 324

             Breadth = √324  = 18 inches

Perimeter of the suitcase  = 2(24 + 18)  = 84 inches.

The length of zipper that will cover this suitcase is 84inches.

Let x = time, weeks.
Let y =  length of Rip van Winkle's beard, mm

Initially, his beard was 888 mm long, therefore
When x = 0, y = 888.

For every week, y increases by 222 mm.
Therefore
y = 222x + 888

This is an equation for a straight line with 
slope = 222,
y-intercept = 888

When x = 1, y = 222 + 888 = 1110 mm
To draw the straight line, choose two points:
(0, 888)  from the y-intercept
(1, 1110)

The graph of the straight line is shown below. The two points are shown on the line.