SOLUTION: A rectangular photo of dimensions 7 cm by 8 cm is placed in a picture frame of uniform width on all sides.The resulting total area (picture and frame) is 182 square cm. What is

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: A rectangular photo of dimensions 7 cm by 8 cm is placed in a picture frame of uniform width on all sides.The resulting total area (picture and frame) is 182 square cm. What is       Log On


   

Question 764333: A rectangular photo of dimensions 7 cm by 8 cm is placed in a picture frame of uniform width on all sides.The resulting total area (picture and frame) is 182 square cm.
What is the width of the picture frame? Set up and solve an equation to answer this question.

Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Let w = width of the frame.

Total area of the frame and picture = %287%2B2w%29%288%2B2w%29=182 which will obviously be quadratic.
Begin to simplify.
56%2B16w%2B14w%2B4w%5E2=182
4w%5E2%2B30w%2B56=182
4w%5E2%2B30w-126=0
2w%5E2%2B15w-63=0

Use general solution unless you see a way to factor if possible.