SOLUTION: Solving Problems with Quadratic Equations 18. A rectangular picture frame measures 20 cm by 30 cm. A new frame is to be made by increasing each side length by the same amount. The

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Solving Problems with Quadratic Equations 18. A rectangular picture frame measures 20 cm by 30 cm. A new frame is to be made by increasing each side length by the same amount. The      Log On


   

Question 198592: Solving Problems with Quadratic Equations
18. A rectangular picture frame measures 20 cm by 30 cm. A new frame is to be made by increasing each side length by the same amount. The resulting enclosed area is to be 1064cm^2. Find the dimensions of the new picture frame. 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%2A30 and a%5B2%5D=1064 where a%5B1%5D is area of the smaller rectangle and a%5B2%5D is the bigger one. x will be the width added to the initial rectangle.
a%5B2%5D=%2820%2Bx%29%2830%2Bx%29 is the new dimensions of the rectangle.
Solve
a%5B1%5D=20%2A30=600a%5B2%5D=1064
Therefore
1064=%2820%2Bx%29%2830%2Bx%29
Solve for x
x%5E2%2B50x%2B600=1064x%5E2%2B50x-464=0
Quad From
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ when a=1, b=50, c=-464
Therefore
Real solutions:
Root 1: -58
Root 2: 8
Since -58 is the wrong idea, the answer is 8.
8cm needs to be added to each side.

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