Factoring ProblemsDate: 8/14/96 at 13:55:0 From: Anonymous Subject: Word Problems Involving Factorization Dear Dr. Math, I am an English teacher trying to teach Algebra 1. I hope you can help me with the following problem. I have been struggling with the chapter on factoring. I have drawn several pictures to try and figure out this problem, but I'm getting nowhere. A photograph is 7 inches long and 5 inches wide. It is surrounded by a border of uniform width. If the area of the border alone is 64 sq. inches, what is the width of the border? Thanks a lot for all your help! Laura Sturman Date: 8/14/96 at 22:50:5 From: Doctor Robert Subject:Word Problems Involving Factorization Draw yourself a diagram of a rectangle 7 inches by 5 inches. Now add a uniform border all around this rectangle. Call the width of this border x. Now we need to find the area of just the border. One way to do it is to draw a square in each corner. The area of one square is x^2, and since there are four of them, these areas add to 4x^2. Now there are four rectangles left. Two of them have the dimension 5 by x and two of them 7 by x. Adding these areas we get 24x. So we have the following equation: 4x^2 + 24x = 64 Subtracting 64 from both sides and dividing all the way through by 4 we get: x^2 + 6x -16 = 0 This factors into (x+8)(x-2) = 0 so that x = -8 or x = 2. We reject the negative solution. Our answer is x = 2. Therefore, the width of the border is 2 inches. -Doctor Robert, The Math Forum Check out our web site! http://mathforum.org/dr.math/ |
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