Question 640394
To answer this question, you'll need to find the height and width of the painting. Let h = the height and w = the width:
The area of the rectangular painting is expressed by:
{{{A = h*w}}} but h = w+16 and A = 720, so making the appropriate substitutions, you get:
{{{720 = (w+16)*w}}} which, after some rearranging looks like:
{{{w^2+16w-720 = 0}}} Do you see how we get this? Now you can factor this quadratic:
{{{(w-20)(w+36) = 0}}} which means that:
{{{w = 20}}} or {{{w = -36}}} Discard the negative solution as the width must be a positive quantity.
So the width is 20 inches and the height is 36 (20+16) inches.
Convert to feet:
Width = 1ft 8in.
Height = 3 ft.
So you can see that the painting will fit in the allocated space.