7.5 Exercises Do the exercises, and check your work. Write an equation, and solve. 9) A rectangular rug is 4 ft longer than it is wide. If its area is 45 ft2, what is its length and width? 10) The surface of a rectangular bulletin board has an area of 300 in2. Find its dimensions if it is 5 in. longer than it is wide. 11) Judy makes stained glass windows. She needs to cut a rectangular piece of glass with an area of 54 in2 so that its width is 3 in. less than its length. Find the dimensions of the glass she must cut. 12) A rectangular painting is twice as long as it is wide. Find its dimensions if it has an area of 12.5 ft2. 13) The volume of a rectangular storage box is 1440 in3. It is 20 in. long, and it is half as tall as it is wide. Find the width and height of the box. 14) A rectangular aquarium is 15 in. high, and its length is 8 in. more than its width. Find the length and width if the volume of the aquarium is 3600 in3. 15) The height of a triangle is 3 cm more than its base. Find the height and base if its area is 35 cm2. 16) The area of a triangle is 16 cm2. Find the height and base if its height is half the length of the base. Objective 2: Solve Problems Involving Consecutive Integers Write an equation, and solve. 17) The product of two consecutive integers is 19 more than their sum. Find the integers. 18) The product of two consecutive odd integers is 1 less than three times their sum. Find the integers. 19) Find three consecutive even integers such that the sum of the smaller two is one-fourth the product of the second and third integers. 20) Find three consecutive integers such that the square of the smallest is 29 less than the product of the larger two. 21) Find three consecutive integers such that the square of the largest is 22 more than the product of the smaller two. Objective 1: Solve Problems Involving Geometry Find the length and width of each rectangle. 1) Area 36 in2 2) Area 40 cm2 x x 9 x 1 x 2 Find the base and height of each triangle. 3) Area 12 cm2 x 6 2x 1 4) Area 42 in2 x 1 2x Find the base and height of each parallelogram. 5) Area 18 in2 x 2 x 1 6) Area 50 cm2 x 2 3x 1 7) The volume of the box is 240 in3. Find its length and width. 3x 1 2x 4 in. 8) The volume of the box is 120 in3. Find its width and height. x 2 x 8 in. www.mhhe.com/messersmith SECTION 7.5 Applications of Quadratic Equations 409
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