Answer to Question #64136 in Geometry for Janette A. Merenillo

Question

2.A right triangle has hypotenuse of length 13 and one leg of length 5. Find the dimensions of the rectangle of largest areas which has one side along the hypotenuse and the ends of the opposite side on the legs of this triangle.
3.A closed box with a square base is to have a volume of 2000 cu. Inches. The material for the top and bottom of the box is to cost Php3 per square inch, and the material, find the dimensions of the box.
1.Find the dimensions of the largest circle that can be inscribed in a square of 12 inches.
1.A manufacturer makes aluminum cups of a given volume ( 16 in3 ) in the form of right circular cylinders open at the top. Find the dimensions which use the least material.
2.Find the dimensions of the right circular cylinder of maximum volume which can be inscribed in a right circular cone of altitude 10 and radius 12.