Math A-100 IUSB Sec. 6.7 Detailed Notes – Week 11 Real Life Applications (i.e. Word Questions) With “real life” applications (i.e. word questions), we are rarely directly given the quadratic equation. Instead we are expected to come up with the equations to use NOTE: Keep in mind that on “real life” scenarios, sometimes the answers we come up with simply will not work. We call these “exclusions”. Example 1: Your living room is 150 square feet in area. Its width is 5 feet shorter than its length. What are the length and the width? Area = length x width Length = L Width is 5 feet shorter than the length = L – 5 Substituting: Area = length x width Solve: 150 = (L)(L – 5) 150 = L2 – 5L 0 = L2 – 5L – 150 0 = (L – 10)(L + 5) 0 = L – 10 L = 10 or L = 10 ft. or becomes 150 = (L)(L – 5) Distribute to get: Set it “=” to 0 Factor to get Use Zero-Factor Property or 0=L+5 L = -5 L = -5 ft. WAIT!!! - How can you have a living room that is -5 feet long??? That solution makes no sense – so exclude it Answer: Length is 10 feet and Width is 5 feet Example 2: You have a right triangle in which one leg is 7 inches longer that the other one. The hypotenuse is 13 inches. Find the length of the two legs. The three sides of a right triangle are related by the Pythagorean Theorem: a2 + b2 = c2 where “a” and “b” are the two legs and “c” is the hypotenuse. Shorter leg = x Longer leg is 7 inches longer = x + 7 Hypotenuse = 13 Plugging them into the Pythagorean Theorem gives us: a2 + b2 = c2 becomes (x)2 + (x + 7)2 = (13)2 Cleaning it up: x2 + x2 + 14x + 49 = 169 Simplifying: 2x2 + 14x + 49 = 169 Set it “=” to 0: 2x2 + 14x -120 = 0 Factoring: 2x2 + 14x -120 = 0  2(x2 + 7x - 60) = 0  2(x + 12)(x – 5) = 0 Zero-Factor Property: x + 12 = 0 or x – 5 = 0 x = -12 or 5 x = -12 in. or x = 5 in.  triangle leg cannot be -12 inches long, so exude it. Answer: x = 5 inches Shorter leg = 5 inches and longer leg = 12 inches