SOLUTION: Solving Problems with Quadratic Equations 22. A photograph measures 21 cm by 15 cm. A strip of constant width is to be cut from each side of the photo, so the area is reduced to 2

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Question 198598: Solving Problems with Quadratic Equations
22. A photograph measures 21 cm by 15 cm. A strip of constant width is to be cut from each side of the photo, so the area is reduced to 216 cm^2. Find the width of the cut. Include a diagram in your solution.
Thanksss
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=21%2A15 and a%5B2%5D=216 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=%2821-x%29%2815-x%29 is the new dimensions of the rectangle.
Solve
a%5B1%5D=21%2A15=315a%5B2%5D=216
Therefore
216=%2821-x%29%2815-x%29
Solve for x
x%5E2-36x%2B315=216x%5E2-36x%2B99=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=99
Therefore
Real solutions:
Root 1: 3
Root 2: 33
Since 33 is a bit to large to take away from 21 or 15, the answer is 3.
3cm 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