Question 66106
Let's find the equation for the area of the poster + frame.
The area of the poster alone is:
{{{A = L*W}}} but the total size with the frame is 4 inches more on each side, so the area then becomes:
{{{A = (L+4)(W+4)}}} and since the length, L = W+4, you can substiute this to get:
{{{A = ((W+4)+4)(W+4)}}} and the total area is given as 672 sq.in, so...
{{{((W+4)+4)(W+4) = 672}}} Simplifying this, you get:
{{{(W+8)(W+4) = 672}}}
{{{W^2 + 12W + 32 = 672}}} Now subtract 672 from both sides.
{{{W^2 + 12W - 640 = 0}}} Now that we have the quadratic equation, we can factor it, if possible:
{{{W^2 + 12W - 640 = (W - 20)(W + 32)}}} so:
{{{(W-20)(W+32) = 0}}}
This does not match exactly any of the given possible answers, does it?