SOLUTION: Solving Problems with Quadratic Equations 23. A photograph measures 20 cm by 16 cm. A strip of constant width is to be cut off the top and one side of the photo, so the area is re

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Solving Problems with Quadratic Equations 23. A photograph measures 20 cm by 16 cm. A strip of constant width is to be cut off the top and one side of the photo, so the area is re      Log On


   

Question 198599: Solving Problems with Quadratic Equations
23. A photograph measures 20 cm by 16 cm. A strip of constant width is to be cut off the top and one side of the photo, so the area is reducedd to 60% of teh area of the original photo. Find the width of the cut. Include a diagram in your solution.
Thanks###!!!
Answer by arallie(162) About Me  (Show Source):
You can put this solution on YOUR website!
I don't know how to a diagram, sorry. But I do have the solution.
a%5B1%5D=20%2A16 and a%5B2%5D=.60a%5B1%5D where a%5B1%5D is area of the uncut rectangle and a%5B2%5D is the smaller one. x will be the width cut from the initial rectangle.
a%5B2%5D=%2820-x%29%2816-x%29 is the new dimensions of the rectangle.
Solve
a%5B1%5D=20%2A16=320a%5B2%5D=.60%28320%29=192
Therefore
192=%2820-x%29%2816-x%29
Solve for x
x%5E2-36x%2B320=192x%5E2-36x%2B128=0
Quad From
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ when a=1, b=-36, c=128
Therefore
Real solutions:
Root 1: 4
Root 2: 32
Since 32 is a bit to large to take away from 20 or 16, the answer is 4.
4cm needs to be cut from each side.

Anymore questions feel free to ask me.
Anthony Allie
arallie@gmail.com
http://arallie.webs.com/tutoring.htm