SOLUTION: A photo is four 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 square inches. what are the dimensions

Question 202688: A photo is four 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 square inches. what are the dimensions of the photo? Can you please help me solve involving applications of polyinomials?
Answer by rajagopalan(174) (Show Source): You can put this solution on YOUR website!
Let the width of Photo=x
Then Length=x+4
Overall length (OL) with border = (x+4)+ 6 ..(twice border size of 3)
Overall width (OB) with border = (x) + 6 ..(twice border size of 3)
Overall area = OL*OB
Overall area = (x+10)*(x+6)
we get area =x^2+16x+60
x^2+16x+60 =165
x^2+16x+60-165=0
x^2+16x-105 =0
Splitting terms
x^2+21x-5x-105=0
x(x+21)-5(x+21)=0
(x-5)(x+21)=0
giving x= 5 or -21.
Ignoring negative value we get x=5
Answer:
Width of Photo=5
Length of photo=5+4=9
***
Verification:
Border size:
=(9+6)*(5+6)=15*11=165 sq units
OKAY
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