Find the base and height of each parallelogram. 5) Area 36 in2 x 2 x 6) Area 240 mm2 x 8 x base 9 in.; height 4 in. base 20 mm; height 12 mm 7) The volume of the box is 648 in3. Find its height and width. x 1 x 2 12 in. height 6 in.; width 9 in. 8) The volume of the box is 6 ft3. Find its width and length. 1.5 ft x 1 x 1 width 2 ft; length 2 ft Write an equation and solve. 9) A rectangular sign is twice as long as it is wide. If its area is 8 ft2, what are its length and width? length 4 ft; width 2 ft 10) An ad in a magazine is in the shape of a rectangle and occupies 88 in2. The length is three inches longer than the width. Find the dimensions of the ad. 8 in. by 11 in. 11) The top of a kitchen island is a piece of granite that has an area of 15 ft2. It is 3.5 ft longer than it is wide. Find the dimensions of the surface. 2.5 ft by 6 ft 12) To install an exhaust fan, a builder cuts a rectangular hole in the ceiling so that the width is 3 in. less than the length. The area of the hole is 180 in2. Find the length and width of the hole. length 15 in.; width 12 in. 13) A rectangular makeup case is 3 in. high and has a volume of 90 in3. The width is 1 in. less than the length. Find the length and width of the case. length 6 in.; width 5 in. 14) An artist’s sketchbox is 4 in. high and shaped like a rectangular solid. The width is three-fourths as long as the length. Find the length and width of the box if its volume is 768 in3. length 16 in.; width 12 in. 15) The height of a triangle is 1 cm more than its base. Find the height and base if its area is 21 cm2. height 7 cm; base 6 cm 16) The area of a triangle is 24 in2. Find the height and base if its height is one-third the length of the base. height 4 in.; base 12 in. Objective 2: Solve Problems Involving Consecutive Integers Write an equation, and solve. 17) The product of two consecutive integers is 13 less than fi ve times their sum. Find the integers. 8 and 9, or 1 and 2 18) The product of two consecutive integers is 10 less than four times their sum. Find the integers. 6 and 7, or 1 and 2 19) Find three consecutive even integers such that the product of the two smaller numbers is the same as twice the sum of all three integers. 6, 8, 10; or 2, 0, 2 20) Find three consecutive even integers such that fi ve times the sum of the smallest and largest integers is the same as the square of the middle number. 8, 10, 12; or 2, 0, 2 21) Find three consecutive odd integers such that the product of the two larger numbers is 18 more than three times the sum of all three numbers. 7, 9, 11 22) Find three consecutive odd integers such that the square of the largest integer is 9 more than six times the sum of the two smaller numbers. 5, 7, 9; or 1, 1, 3 Objective 3: Solve Problems Using the Pythagorean Theorem 23) In your own words, explain the Pythagorean theorem. Answers may vary. 24) Can the Pythagorean theorem be used to fi nd a in this triangle? Why or why not? a 11 12 No; it is not a right triangle. Use the Pythagorean theorem to fi nd the length of the missing side. 25) 15 12 26) 9 17 8 15 www.mhhe.com/messersmith SECTION 7.6 Applications of Quadratic Equations 439
messersmith_power_introductory_algebra_1e_ch4_7_10
To see the actual publication please follow the link above