Answer
$2\ in$
Work Step by Step
Step 1. Draw a diagram as shown in the figure, where $x$ is the width of the frame.
Step 2. The larger rectangle has dimensions $10+2x$ and $16+2x$
Step 3. The area of the large rectangle is given by $(10+2x)(16+2x)=280$ or $(5+x)(8+x)=70$, which gives $x^2+13x-30=0$
Step 4. Factor the above equation to get $(x+15)(x-2)=0$, and choose the positive solution to get $x=2\ in$
