148 CHAPTER 1 Equations and Inequalities Solve each problem. See Examples 1 and 2. 19. Dimensions of a Right Triangle The lengths of the sides of a right triangle are consecutive even integers. Find these lengths. (Hint: Use the Pythagorean theorem.) 20. Dimensions of a Right Triangle The lengths of the sides of a right triangle are consecutive positive integers. Find these lengths. (Hint: Use the Pythagorean theorem.) 21. Dimensions of a Square The length of each side of a square is 3 in. more than the length of each side of a smaller square. The sum of the areas of the squares is 149 in.2. Find the lengths of the sides of the two squares. 22. Dimensions of a Square The length of each side of a square is 5 in. more than the length of each side of a smaller square. The difference of the areas of the squares is 95 in.2. Find the lengths of the sides of the two squares. Solve each problem. See Example 1. 23. Dimensions of a Parking Lot A parking lot has a rectangular area of 40,000 yd2. The length is 200 yd more than twice the width. Find the dimensions of the lot. 24. Dimensions of a Garden An ecology center wants to set up an experimental garden using 300 m of fencing to enclose a rectangular area of 5000 m2. Find the dimensions of the garden. x is in meters. 150 – x x 25. Dimensions of a Rug Zachary wants to buy a rug for a room that is 12 ft wide and 15 ft long. He wants to leave a uniform strip of floor around the rug. He can afford to buy 108 ft2 of carpeting. What dimensions should the rug have? 12 ft 15 ft 108 ft2 26. Width of a Flower Border A landscape architect has included a rectangular flower bed measuring 9 ft by 5 ft in her plans for a new building. She wants to use two colors of flowers in the bed: one in the center and the other for a border of the same width on all four sides. If she has enough plants to cover 24 ft2 for the border, how wide can the border be? 27. Volume of a Box A rectangular piece of metal is 10 in. longer than it is wide. Squares with sides 2 in. long are cut from the four corners, and the flaps are folded upward to form an open box. If the volume of the box is 832 in.3, what were the original dimensions of the piece of metal? 28. Volume of a Box In Exercise 27, suppose that the piece of metal has length twice the width, and 4-in. squares are cut from the corners. If the volume of the box is 1536 in.3, what were the original dimensions of the piece of metal?
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