119 1.2 Applications and Modeling with Linear Equations 13. Dimensions of a Puzzle Piece A puzzle piece in the shape of a triangle has perimeter 30 cm. Two sides of the triangle are each twice as long as the shortest side. Find the length of the shortest side. (Side lengths in the figure are in centimeters.) 14. Dimensions of a Label The length of a rectangular label is 2.5 cm less than twice the width. The perimeter is 40.6 cm. Find the width. (Side lengths in the figure are in centimeters.) 15. Perimeter of a Plot of Land The perimeter of a triangular plot of land is 2400 ft. The longest side is 200 ft less than twice the shortest. The middle side is 200 ft less than the longest side. Find the lengths of the three sides of the triangular plot. 16. World’s Largest Ice Cream Cake The world’s largest ice cream cake, a rectangular cake made by a Dairy Queen in Toronto, Ontario, Canada, on May 10, 2011, had length 0.39 m greater than its width. Its perimeter was 17.02 m. What were the length and width of this 10-ton cake? (Data from www.guinnessworldrecords.com) 17. Storage Bin Dimensions A storage bin is in the shape of a rectangular box. Find the height of the box if its length is 18 ft, its width is 8 ft, and its surface area is 496 ft2. (In the figure, h = height. Assume that the given surface area includes that of the top lid of the box.) 18 ft 8 ft h 18. Cylinder Dimensions A right circular cylinder has radius 6 in. and volume 144pin.3. What is its height? (In the figure, h = height.) h is in inches. h 6 in. x 2x 2x w 2w – 2.5 HOME FINDERS 55 North Maple St. Philadelphia, PA 19106 HF Solve each problem. See Example 2. 19. Distance to an Appointment Margaret drove to a business appointment at 50 mph. Her average speed on the return trip was 40 mph. The return trip took 1 4 hr longer because of heavy traffic. How far did she travel to the appointment? 20. Distance between Cities Elwyn averaged 50 mph traveling from Denver to Minneapolis. Returning by a different route that covered the same number of miles, he averaged 55 mph. What is the distance between the two cities to the nearest ten miles if his total traveling time was 32 hr? r t d Morning 50 x Afternoon 40 x + 1 4 r t d Going 50 x Returning 55 32 - x
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