SOLUTION: steve's photograph is thrice as long as it is wide. It mounted so that a border 2cm wide completely surrounds the photograph. Find the dimensions of the photograph if the area

Algebra ->  Customizable Word Problem Solvers  -> Geometry -> SOLUTION: steve's photograph is thrice as long as it is wide. It mounted so that a border 2cm wide completely surrounds the photograph. Find the dimensions of the photograph if the area      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 1022746: steve's photograph is
thrice as long as it is wide. It
mounted so that a border 2cm wide
completely surrounds the
photograph. Find the dimensions of
the photograph if the area of the
border is 200 cm squared
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
Picture is x by 3x.
Picture's area is 3x^2.

Border has uniform width, surrounding the picture, 2 cms.

Total area is %28x%2B2%2A2%29%283x%2B2%2A2%29
%28x%2B4%29%283x%2B4%29.

JUST the area of the border is 200 SQUARE CENTIMETERS.
JUST the area of the border is highlight_green%28%28x%2B4%29%283x%2B4%29-3x%5E2=200%29.
Simplify and solve this equation. You will have x from which to evaluate 3x.

Steps from there:
3x%5E2%2B12x%2B4x%2B16-3x%5E2=200
16x%2B16=200
16x=184
2x=23
highlight%28x=23%2F2%29, and you can find 3x from this.