The rectangular top surface of a patio is 4 feet longer than it is wide and has an area of 192 square feet. What is the width, in feet, of the rectangular top surface of the patio?

Summary Submit Skip Question

The rectangular top is 4 feet longer than it is wide.

$$ l = 4+w $$ $$ A= lw $$ $$ 192 = (4+w)w $$ $$ 192 = 4w+w^2 $$

We can solve for the width in the calculator by setting the graph \(y=192\) and \(y=4w+w^2\) and check for intersections. Alternatively,

$$ 192=4w+w^2 $$ $$ w^2+4w-192 = 0 $$ $$ (w-12)(w+16) = 0 $$ $$ w= \boxed{12}$$