 The product of two consecutive negative integers is 1122. What are the numbers?

A garden measuring 12 meters by 16 meters is to have a pedestrian pathway installed all
around it, increasing the total area to 285 square meters. What will be the width of the
pathway?

You have to make a square-bottomed, unlidded box with a height of three inches and a
volume of approximately 42 cubic inches. You will be taking a piece of cardboard, cutting
three-inch squares from each corner, scoring between the corners, and folding up the
edges. What should be the dimensions of the cardboard, to the nearest quarter inch?
I try to offer some help here!
When dealing with geometric sorts of word problems, it is
usually helpful to draw a picture. Since I'll be cutting
equal-sized squares out of all of the corners, and since
the box will have a square bottom, I know I'll be starting
with a square piece of cardboard.
I don't know how big the cardboard will be yet, so I'll label
the sides as having length "w".
Since I know I'll be cutting out three-by-three squares to
get sides that are three inches high, I can mark that on
my drawing.
The dashed lines show where I'll be scoring the
cardboard and folding up the sides.
Since I'll be losing three inches on either end of the
cardboard when I fold up the sides, the final width of the
bottom will be the original "w" inches, less three on the
one side and another three on the other side. That is, the
width of the bottom will be w – 3 – 3 = w – 6.