A picture frame measures $14$cm by $20$cm. $160$cm$^2$ of the picture shows inside the frame. Find the width of the frame.

Question

A picture frame measures $14$cm by $20$cm. $160$cm$^2$ of the picture shows inside the frame. Find the width of the frame.

I know how to interpret it now, but how do I solve it? The equation I made from this is $$(14-2x)(20-2x)=\frac 23\cdot14\cdot20$$which solves into $$x = \dfrac{17\pm\sqrt{\dfrac{587}3}}{2}$$but this looks incorrect

Answer 1

Turning comment into answer per request.

The LHS of your equation is good, but the RHS should be $160$ (that's the area after all!). We'd have $$(14-2x)(20-2x)=160$$ which we may simplify to $$(7-x)(10-x)=40$$ Eyeballing it yields $x=2$.

Answer 2

If $h$ is the width of the frame then:

\begin{equation} 120=2(14-2h)h+2(20-2h)h+4h^2 \end{equation}

where 120 is the area of the frame. $4h^2$ is the area of the corners (they are squares), the other terms represent the area of the four rectangles left.