find the length of rectangle based on area of frame A rectangular picture is $3$ cm longer than its width, $(x+3)$. A frame $1$ cm wide is placed around the picture. The area of the frame alone is $42 \text{cm}^2$. Find the length of the picture.
I have tries: 
$(x+6)(x+3) = 42 \\
x^2+3x+6x+12 = 42 \\
x^2+9x+12x-42 = 0 \\
\\
x^2 + 21 -42$

Area $A$ of the $1$-cm-wide frame in cm$^2$ is $2\times $ height $+ 2\times $ width $+ 4$ (for the corners).
$A = 2 (x+3) + 2(x+6)+4 = 4x+22 = 42$
$\implies x=5$
The length is $(x+6) = 11$ cm 
