AFM Wkst 4C.4 Name_________________________________ Solve each. 1. The sum of the squares of two consecutive even integers is 1252. Find the integers. 2. A rectangular garden is 10 ft longer than it is wide. Its area is 875 sq. ft. What are its dimensions? 3. A rectangular bedroom is 7 ft longer than it is wide. Its area is 228 sq. ft. What is the width of the room? 4. The Goldsteins are planning to add a rectangular porch to their house. The width of the porch will be 4 feet less than its length, and they want it to have an area of 96 square feet. Find the length and width of the porch. 5. The area of a parallelogram is 45 square units. Find its base and its height. 6. Ed and Mark leave their office with Ed traveling north and Mark traveling east. When Mark is 1 mile farther than Ed from the office, the distance between them is 2 miles more than Ed’s distance from the office. Find their distances from the office and the distance between them. 7. The length of a VHS videocassette shell is 3 inches more than its width. The area of the rectangular top side of the shell is 28 square inches. Find the length and the width of the videocassette shell. 8. A plastic box that holds a standard audiocassette has a length 4 centimeters longer than its width. The area of the rectangular top of the box is 77 square centimeters. Find the length and width of the box. 9. The area of a triangle is 30 square inches. The base of the triangle measures 2 inches more than twice the height of the triangle. Find the measures of the base and the height. 10. A garden has the shape of a right triangle with one leg 2 meters longer than the other. The hypotenuse is two meters less than twice the length of the shorter leg. Find the length of the shorter leg. 15. Craig Hoffman wants to build a swimming pool surrounded by a sidewalk of uniform width. He wants the dimensions of the entire pool and sidewalk area to be 16 m by 20 m. The pool has an area of 192 sq. meters. How wide should the sidewalk be? 11. The product of two consecutive integers is 11 more than their sum. Find the integers. 16. As an object is propelled upwards, at an initial velocity of 80 feet per second, gravity pulls it back to Earth. This relationship can be modeled by h= –16t2 + 80t. Find how long it would take for the object to return to Earth. 12. Find three consecutive odd integers such that 3 times the sum of all three is 18 more than the product of the smaller two. 17. A photo editor at a magazine has a 12.5 cm by 8.4 cm photo of a rabbit sitting in the center of a large field of grass. She wishes to get a print that has half the area of the original photo and concentrates on the rabbit. The layout artist needs to be told how much of the grass section to crop, or cut off. If the same amount is cropped from all edges of the photo, what are the dimensions of the print? 18. The Jacksonville Athletic Association owns a large lot. On a portion of the lot, a square athletic field has been maintained. Each side of the field is 110 feet long. The association would like to equally expand two of the sides of the field for parking spaces so that the entire region has an area of 14,000 ft2. What is the width of the parking strips being added? 13. 14. The length of a rectangle is 6 meters more than the width. The area is 40 square meters. Find the length and width of the rectangle. The sides of a right triangle have lengths (in feet) that are consecutive integers. What are the lengths of the sides?