## 32 - 34 Maxima and minima problems of a rectangle inscribed in a triangle

**Problem 32**

Find the dimension of the largest rectangular building that can be placed on a right-triangular lot, facing one of the perpendicular sides.

**Problem 32**

Find the dimension of the largest rectangular building that can be placed on a right-triangular lot, facing one of the perpendicular sides.

**Problem 29**

The sum of the length and girth of a container of square cross section is a inches. Find the maximum volume.

**Problem 28**

The perimeter of an isosceles triangle is P inches. Find the maximum area.

**Problem 25**

Find the most economical proportions of a quart can.

**Problem 21**

Find the rectangle of maximum perimeter inscribed in a given circle.

**Problem 18**

The strength of a rectangular beam is proportional to the breadth and the square of the depth. Find the shape of the largest beam that can be cut from a log of given size.

**Problem 15**

A box is to be made of a piece of cardboard 9 inches square by cutting equal squares out of the corners and turning up the sides. Find the volume of the largest box that can be made in this way.

**Problem 12**

A rectangular field of fixed area is to be enclosed and divided into three lots by parallels to one of the sides. What should be the relative dimensions of the field to make the amount of fencing minimum?

**Problem 9**

What should be the shape of a rectangular field of a given area, if it is to be enclosed by the least amount of fencing?