Peter bought a special pen as a birthday present for an artist friend. He has a sturdy box that he wants to use to mail the pen. The box is 4 inches wide, 2 inches deep, and 8 inches high. The pen is 10 inches long. Peter knows he will have to place it in the box along the “long” diagonal AB, as shown in the diagram. Will the pen fit in the box? (Ignore the thickness of the pen.) Give the length of the long diagonal and explain how you found your answer. The box is 4 inches wide, 2 inches deep, and 8 inches high. The pen is 10 inches long. Peter knows he will have to place it in the box along the “long” diagonal AB, as shown in the diagram. Will the pen fit in the box? (Ignore the thickness of the pen.) Give the length of the long diagonal and explain how you found your answer. Peter bought a special pen as a birthday present for an artist friend. He has a sturdy box that he wants to use to mail the pen. The box is 4 inches wide, 2 inches deep, and 8 inches high. The pen is 10 inches long. Peter knows he will have to place it in the box along the “long” diagonal AB, as shown in the diagram. Will the pen fit in the box? (Ignore the thickness of the pen.) Give the length of the long diagonal and explain how you found your answer. Begin by finding the length of AC using right triangle ADC. Then use the fact that angle ACB is a right angle. You may want to use a shoe box or another box-shaped object to help you picture the situation.
PythBox1 2. Generalize your findings from Questions 1 and 2 to a box with dimensions p, q, and r units. In other words, find the length from U to V, as shown in the diagram?