Question 178300: A photo is 4 inches longer than its width. A 3 inch border is placed around the photo making the total area around the photo and border 165 square inches. What are the dimensions of the photo
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! A photo is 4 inches longer than its width. A 3 inch border is placed around the photo making the total area around the photo and border 165 square inches. What are the dimensions of the photo?
:
Let x = width of the photo
then
(x+4) = length of the photo
:
draw this out showing the 3" border around the photo, label the photo width as
x and the length as (x+4), and you will see the dimensions of the rectangle
including the 3" border are (x+6) by (x+4+6) or (x+10)
:
Overall area given as 165 sq/in so we have:
Length * width = 165 sq/in
(x+10)*(x+6) = 165
FOIL
x^2 + 6x + 10x + 60 = 165
:
x^2 + 16x + 60 - 165 = 0
:
x^2 + 16x - 105 = 0; our old friend, the quadratic equation!
Factors to
(x+21)(x-5) = 0
positive solution is what we want here:
x = 5" is the width of the photo
and
5 + 4 = 9" is the length
;
;
Check solution by confirming the overall area:
(5+6)*(9+6) =
11 * 15 = 165
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