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29) The height of a triangular sail is 1 ft less than twice the base of the sail. Find its height and the length of its base if the area of the sail is 60 ft2. 30) Chandra cuts fabric into isosceles triangles for a quilt. The height of each triangle is 1 in. less than the length of the base. The area of each triangle is 15 in2. Find the height and base of each triangle. 31) Valerie makes a bike ramp in the shape of a right triangle. The base of the ramp is 4 in. more than twice its height, and the length of the incline is 4 in. less than three times its height. How high is the ramp? x 2x x 32) The width of a widescreen TV is 10 in. less than its length. The diagonal of the rectangular screen is 10 in. more than the length. Find the length and width of the screen. x 1 x x 1 Objective 4: Solve an Applied Problem Using a Quadratic Equation Solve. 33) An object is propelled upward from a height of 4 ft. The height h of the object (in feet) t sec after the object is released is given by h 16t2 60t 4 a) How long does it take the object to reach a height of 40 ft? b) How long does it take the object to hit the ground? 34) An object is launched from the ground. The height h of the object (in feet) t sec after the object is released is given by h 16t2 64t When will the object be 48 ft in the air? 21) da2 ha k for a 22) kt2 mt n for t 23) s 1 2 gt2 vt for t 24) s 2prh pr2 for r Mixed Exercises: Objectives 2 and 3 Write an equation, and solve. 25) The length of a rectangular piece of sheet metal is 3 in. longer than its width. A square piece that measures 1 in. on each side is cut from each corner, then the sides are turned up to make a box with volume 70 in3. Find the length and width of the original piece of sheet metal. 26) The width of a rectangular piece of cardboard is 8 in. less than its length. A square piece that measures 2 in. on each side is cut from each corner, then the sides are turned up to make a box with volume 480 in3. Find the length and width of the original piece of cardboard. 27) A rectangular swimming pool is 60 ft wide and 80 ft long. A nonskid surface of uniform width is to be installed around the pool. If there is 576 ft2 of the nonskid material, how wide can the strip of the nonskid surface be? ft ft 28) A picture measures 10 in. by 12 in. Emilio will get it framed with a border around it so that the total area of the picture plus the frame of uniform width is 168 in2. How wide is the border? 12 1 www.mhhe.com/messersmith SECTION 10.4 Formulas and Applications 651


messersmith_power_intermediate_algebra_1e_ch4_7_10
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