To get a picture of this box, draw a line representing the depth. This is 21", but there's no need to draw to scale. At one end of the line, which we'll say represents the front of the box, draw a perpendicular representing the front width of 32". At the other end of the line draw another perpendicular representing the back width of 18". Join the tops of the two perpendiculars. Along the 21" line between the perpendiculars, mark off 15.75" from the front end (the taller perpendicular). Draw a line parallel to the 21" line from the top of the back perpendicular to meet the front perpendicular. What you should see now is a right-angled triangle sitting on top of a rectangle. Where we marked off 15.75" along the 21" line draw a perpendicular till it meets the hypotenuse of the triangle. The length of that perpendicular represents the width of the box at 15.75" deep. We can see straight away that it's more than 18" long because it passes through the rectangle and the triangle. Now look at the triangle. Its base is 21" long; its height is 32-18=14", the difference between the front and back widths. We have two similar right-angled triangles, which will enable us to find the width at 15.75" deep. Let x be the difference between the width at depth 15.75" and the shorter side of the rectangle, 18". The ratios of the sides gives us x/14=15.75/21 (similar figures, using the ratios of the sides of the right-angled triangles). So x=14*15.75/21=2*15.75/3=31.5/3=10.5". We now add this to 18=28.5" as the width at 15.75" depth.