# Worksheet #15 (3.4) - Iowa State University ### Supplemental Instruction Iowa State University

Leader: Kim Course: Math 165 Instructor: Johnston Date: 10/14/12 Use the steps on page 167 of your textbook to find the solution to each practical problem. 1.

(3.4.2)For what number does the principal square root exceed eight times the number by the largest amount? The principal square root is the positive square root. For example the principal square root of 9 is 3, although both -3 and 3 are the square roots of 9. 2.

(3.4.8)Show that for a rectangle of given perimeter K the one with maximum area is a square. 3.

(3.4.10)A farmer has 80 feet of fence with which he plans to enclose a rectangular pen along one side of his 100-foot barn. The side along the barn needs no fence. What are the dimensions of the pen that has the maximum amount of area? 4.

(3.4.14)A farmer wishes to fence off three identical adjoining rectangular pens, each with 300 square feet of area. What should the width and length of each pen be so that the least amount of fence is required? 5.

(3.4.34)A fence h feet high runs parallel to a tall building and w feet from it. Find the length of the shortest ladder that will reach from the ground across the top of the fence to the wall of the building. 1060 Hixson-Lied Student Success Center  515-294-6624  [email protected]  http://www.si.iastate.edu