SOLUTION: A photo is 3 inches longer than it is wide. A 2 inch border is placed around the photo making the total area of the photo and border 108 square inches. What are the dimensions of

Algebra ->  Customizable Word Problem Solvers  -> Geometry -> SOLUTION: A photo is 3 inches longer than it is wide. A 2 inch border is placed around the photo making the total area of the photo and border 108 square inches. What are the dimensions of      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 151709: A photo is 3 inches longer than it is wide. A 2 inch border is placed around the photo making the total area of the photo and border 108 square inches. What are the dimensions of the photo?
Answer by jojo14344(1513) About Me  (Show Source):
You can put this solution on YOUR website!
Okay, since our basis on the highlight%28L%29ength which is 3 inches longer than the highlight%28W%29idth, let x=highlight%28W%29, unknown?
Then, highlight%28L%29=x%2B3
Now, adding 2 inches border around it, so the W becomes x%2B2%28top%29%2B2%28bottom%29. Also the L becomes x%2B3%2B2%28left%29%2B2%28right%29
.
Putting this into equation with Area of the photo+border:
A=L%2AW
108=%28x%2B7%29%28x%2B4%29 ------------> eqn 1
x%5E2%2B11x%2B28-108=0 --------> x%5E2%2B11x-80=0
By Quadratic Formula: a=1%2C+b=11%2C+c=-80
x=%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F2a
x=%28-11%2B-sqrt%2811%5E2-4%2A1%2A-80%29%29%2F2%2A1
x=%28-11%2B-sqrt%28121%2B320%29%29%2F2 -----------> x=%28-11%2B-sqrt%28441%29%29%2F2
x=%28-11%2B-21%29%2F2
x=%28-11%2B21%29%2F2 ---------> x=10%2F2=5
x=%28-11-21%29%2F2 ----------> x=-32%2F2=-16
USE x=5inches
For the dimensions of the photo: highlight%28W%29idth=+5+inches
And, highlight%28L%29ength=5%2B3=8inches
In doubt? Go back eqn 1,
108=%285%2B7%29%285%2B4%29
108=%2812%29%289%29
108=108
Thank you,
Jojo