Question 178284
Length of photo+frame: {{{x+4+6=x+10}}} Width of photo+frame: {{{x+6}}}

Area of photo+frame: {{{A=(x+10)(x+6)}}}


{{{A=(x+10)(x+6)}}} Start with the given equation.


{{{165=(x+10)(x+6)}}} Plug in {{{A=165}}}


{{{165=x^2+16x+60}}} FOIL


{{{0=x^2+16x-105}}} Subtract 165 from both sides.


{{{0=(x+21)(x-5)}}} Factor


{{{x+21=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).