Philip was asked to find the number of vertices of a polyhedron with 32 faces and 60 edges. What is his error?

Find the maximum area of a rectangle that is inside of the triangle formed by the x-axis and the lines y=-3x + 12 and y = 3x + 12. The base of the rectangle is on the x-axis and the two upper vertices are on the lines y=-3x + 12 and y = 3x + 12 as shown in the illustration.

You have 272 feet of fencing and would like to build a playpen for your two show poodles.  The poodles will tear each other's fur out if they are left alone together, so you plan on making a rectangular playpen with a divider down the middle.    What should the dimensions be so that each of your poodles will have the most area to play in?

A fence is to be built to enclose a rectangular area of 300 square feet. The fence along three sides is to be made of material that costs 4 dollars per foot, and the material for the fourth side costs 16 dollars per foot. Find the dimensions of the enclosure that is most economical to construct. Dimensions: 8.66 X 34