A rectangular parallelepiped has edges with integral lengths *x*, *y*, and *z*. The sum of the lengths of all twelve edges is 72 inches. The sum of the areas of all 6 faces is 212 square inches. The volume of the solid is 144 cubic inches. Find the length in inches of a diagonal of this solid.

## Pre-Calculus

## Clock Hands Overlap After Noon

At what time, exactly, do the two hands of a clock overlap for the first time after 12:00 noon?

## Barber Pole

The revolving portion of a splendid barber pole is a cylinder 4 feet tall and 6 inches in radius. The red stripe is painted in a spiral around the cylinder and makes exactly 8 complete turns around it from bottom to top. How long is the stripe? (Ignore its width.)

## Circle Around 3 Squares

The radius of the smallest circle containing the symmetric figure composed of the three squares shown at the right is:

- √2
- √1.25
- 1.25
- 5√17

16 - none of these

## Area of Obtuse Triangle

In an obtuse triangle, the degree measure of one of the acute angles is 45°, and the length of the shortest altitude is 5 inches. If the perimeter of this triangle is 30 + 5√2 inches, find in square inches the area of the triangle.

## Distance

You and a friend are each flying your own small jet airplane. You both take off from Cleveland Hopkins Airport at 12:00 noon. You are traveling due east and your friend is traveling due south. You are traveling at *x* miles per hour and your friend is traveling at *y* miles per hour. Use the Pythagorean Theorem to make up a formula for how far apart your two planes are after *t* hours of flying.

## Fences in Circular Region

In a circular field, place three fences to make four regions. The fences are all equal in length and their endpoints are on the circular boundary of the field. The four resulting regions have equal area, and the fences don�t intersect within the field.

## Split Area of 2 Parallelograms

Two parallelograms are drawn at random on a page (i.e., in a plane). Describe how to draw a single line that will divide each parallelogram into two regions having equal area.

## Hexagon, Triangle Area

An equilateral triangle and a regular hexagon have perimeters of the same length. If the triangle’s area is 2 square units, what is the area of the hexagon? Unless you’re a budding John Von Neuman, it isn’t necessary to calculate areas and then divide. That’s the hard way.

## Overlapping Equilateral Triangles

Two congruent equilateral triangles are placed so that their overlap is a regular hexagon. The triangles each have area 24 sq. cm. What is the area of the hexagon?