SOLUTION: A photo is 4 inches longer than it is wide. A 3 inch border is placed around the photo making the total area of the photo and border 165 inches. What are the dimensions of the ph

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equation Customizable Word Problems -> SOLUTION: A photo is 4 inches longer than it is wide. A 3 inch border is placed around the photo making the total area of the photo and border 165 inches. What are the dimensions of the ph      Log On


   

Question 178284: A photo is 4 inches longer than it is wide. A 3 inch border is placed around the photo making the total area of the photo and border 165 inches. What are the dimensions of the photo?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Length of photo+frame: x%2B4%2B6=x%2B10 Width of photo+frame: x%2B6
Area of photo+frame: A=%28x%2B10%29%28x%2B6%29

A=%28x%2B10%29%28x%2B6%29 Start with the given equation.

165=%28x%2B10%29%28x%2B6%29 Plug in A=165

165=x%5E2%2B16x%2B60 FOIL

0=x%5E2%2B16x-105 Subtract 165 from both sides.

0=%28x%2B21%29%28x-5%29 Factor

x%2B21=0 or x-5=0 Set each factor equal to zero

x=-21 (we'll toss this solution) or x=5 Solve for "x"

So the width of the photo is 5 inches which means that the length of the photo is 9 inches (just add 4 to the width).