SOLUTION: A rectangular portrait is 3 inches longer than it is wide. A 3 inch frame of uniform width is to be placed around the portrait. The area of the portrait and frame is 108in^2. Find

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: A rectangular portrait is 3 inches longer than it is wide. A 3 inch frame of uniform width is to be placed around the portrait. The area of the portrait and frame is 108in^2. Find       Log On


   

Question 757744: A rectangular portrait is 3 inches longer than it is wide. A 3 inch frame of uniform width is to be placed around the portrait. The area of the portrait and frame is 108in^2. Find the dimensions of the portrait without the frame.
Answer by sachi(548) About Me  (Show Source):
You can put this solution on YOUR website!
letbthe width is x" then the length is x+3"
A 3 inch frame of uniform width is to be placed around the portrait i.e on both length & width will increase by 3"
so the dimension of the portrait with frame will be L=x+3+3" & W=x+3"
so the area=(x+3)(x+6)=108
or x^2+9x+18=108
or x^2+9x-90=0
or x^2+15x-6x-90=0
or x(x+15)-6(x+15)=0
or (x+15)(x-6)=0
or x=6 or -15
so x= 6 rejecting -ve value
so the dimensions of the portrait without the frame w=6" & l=6+3=9"