The width of the given photo frame is required.
The width of the frame is 3 inches.
Length of picture = 3 inches
Width of picture = 2 inches
x = Thickness of frame
Length of frame with photo = [tex]3+2x[/tex]
Width of frame with photo = [tex]2+2x[/tex]
The area of frame and picture = 72 square inches
Area is given by
[tex](3+2x)(2+2x)=72\\\Rightarrow 6+6x+4x+4x^2=72\\\Rightarrow 4x^2+10x-66=0\\\Rightarrow x=\dfrac{-10\pm \sqrt{10^2-4\times4\left(-66\right)}}{2\times4}\\\Rightarrow x=3,-\dfrac{11}{2}[/tex]
The width of the frame is 3 inches.
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